Answer:
a) UNIT PRICE of potatoes is $0.56
b) UNIT PRICE of broccoli is $3.1
c) UNIT PRICE of broccoli is $0.98
Step-by-step explanation:
UNIT PRICE is defined as the price of 1 unit.
[tex]\textrm{Unit Price} = \frac{\textrm{Total cost on n products}}{\textrm{n}}[/tex]
Now, here in the given question:
1. Cost of 4.5 pounds of potatoes is $2.52
So, the unit price of potatoes [tex]= \frac{\textrm{2.52}}{\textrm{4.5}} = 0.56[/tex]
⇒ 1 pound of potatoes cost $0.56
Hence,UNIT PRICE of potatoes is $0.56
2 Cost of 2.5 pounds of broccoli is $7.75.
So, the cost of 1 pound of broccoli [tex]= \frac{\textrm{7.75}}{\textrm{2.5}} = 3.1[/tex]
⇒ 1 pound of broccoli cost $3.1
Hence,UNIT PRICE of broccoli is $3.1
3. Cost of 2.5 pounds of pears is $2.45.
So, the cost of 1 pound of pears [tex]= \frac{\textrm{2.45}}{\textrm{2.5}} = 0.98[/tex]
⇒ 1 pound of pears cost $0.98
Hence,UNIT PRICE of broccoli is $0.98
Answer:
Potatoes - $0.56/pound.
Broccoli - $3.1/pound.
Pears - $0.98/pound.
Step-by-step explanation:
A shopper paid $2.52 for 4.5 pounds of potatoes.
So, the unit price of potatoes is [tex]\frac{2.52}{4.5} = 0.56[/tex] dollars per pound.
A shopper paid $7.75 for 2.5 pounds of broccoli.
So, the unit price of broccoli is [tex]\frac{7.75}{2.5} = 3.1[/tex] dollars per pound.
A shopper paid $2.45 for 2.5 pounds of pears.
So, the unit price of pears is [tex]\frac{2.45}{2.5} = 0.98[/tex] dollars per pound. (Answer)
(-10, -10) and (-2, -3) find the slope.
The town of new London uses about 2,750,000 gallons of water each month. If the population of new London is approximately 61,000, which of the following provides the best estimate of the number of gallons of water used per person each month?
45 gallons of water used per person each month
Solution:
Given that,
The town of new London uses about 2,750,000 gallons of water each month
The population of new London is approximately 61,000
To find: Number of gallons of water used per person each month
From given,
Total gallons of water each month = 2750000
Population = 61000
Therefore,
[tex]Gallons\ of\ water\ per\ person = \frac{\text{Total gallons of water each month}}{population}[/tex]
[tex]Gallons\ of\ water\ per\ person = \frac{2750000}{61000}\\\\Gallons\ of\ water\ per\ person = \frac{2750}{61}\\\\Gallons\ of\ water\ per\ person =45.08 \approx 45[/tex]
Thus 45 gallons of water used per person each month
The point P(2, 5) is reflected over the x-axis. What are the coordinates of the resulting point, P′?
Answer:
(2,-5)
Step-by-step explanation:
P(2,5)
(x,y)
Reflection over x-axis so the x coordinate stays the same while the y coordinate changes from a positive to a negative.
The point P(2, 5) reflected over the x-axis will have coordinates (2, -5), as the x-coordinate remains unchanged and the y-coordinate becomes negative.
Explanation:When the point P(2, 5) is reflected over the x-axis, the x-coordinate remains the same while the y-coordinate changes sign. Therefore, the coordinates of the resulting point, P', after reflection would be (2, -5). This is because reflecting over the x-axis means that we keep the horizontal position of the point the same (same x-coordinate), but flip the vertical position (change the sign of the y-coordinate).
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A Hot air balloon is 750 feet high. It descends 325 feet.
Answer:
425
Step-by-step explanation:
just subtract, 750-325
You subtract 750 - 325 = 425. Your answer is 425.
Hope this helps!!!!!
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Which of the following numbers are greater than -0.33?
Choose all that apply:
A.-0.3
B. -3/9
C. 1/6
Answer:
A: -0.3 and C: 1/6
Step-by-step explanation:
Step 1. Since 1/6 is positive it is greater than all negative numbers including -0.33
Step 2. -0.33 and -0.3 have the same numbers they are both negative but in -0.33 there are more hundred.
-0.3 >- 0.33
Step 3. -3/9= 0.33333..... -0.33 and -3/9 have the same number of units, tenths and hundredths and both are negative but, -3/9 has more thousandths, so it's farther below 0.
-3/9 < -0.33
Final Step 4. -0.3 and 1/6 are greater than-0.33
The correct options are A.-0.3 and C. 1/6
What is a number line in mathematics?In mathematics, an interval can be defined as a set of real numbers that contains all real numbers lying within any two specific numbers of the set R.
Given here: -0.33 which is equivalent to -1/3
The numbers greater than -1/3 lie in the interval (-1/3, ∞)
Clearly out of the given options only -0.3 and 1/6 lie in this interval.
Hence, The correct options are A.-0.3 and C. 1/6
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D={[x, f(x)]: (-1,3), (0, 2), (1, 3), (2, 6), (3, 11)]
Write the rule for f(x).
Answer:
f(x) = x² +2
Step-by-step explanation:
x-values are evenly spaced, and y-values decrease to a minimum of 2, then increase again. First differences are -1, 1, 3, 5, and second differences are constant at 2. This means that a 2nd degree polynomial can be used for the rule.
The minimum of f(x) occurs at x=0, so there is no horizontal shift of the vertex of the quadratic function. f(1) -f(0) = 1, so the vertical scale factor for the quadratic is 1.
The quadratic with a vertex of (0, 2) and a vertical scale factor of 1 is ...
f(x) = 1·(x -0)² +2
f(x) = x² +2 . . . . . . simplified
_____
Comment on differences
"First differences" are the differences between successive "y" values when the "x" values are evenly spaced. Here, they are 2-3 = -1, 3-2 = 1, 6-3 = 3, 11-6 = 5. These are not constant, so the function is not a linear function.
"Second differences" are the differences between successive first differences. Here, they are 1-(-1) = 2, 3-1 = 2, 5-3 = 2. These are constant, so the function is a quadratic (2nd-degree). When n-th differences are constant, the sequence can be modeled by a polynomial of degree n.
__
Comment on determining the rule
Once you know the rule is 2nd-degree, there are a number of ways you can find out what it is. One way is to write it as ...
f(x) = ax^2 + bx + c
and fill in three different values for x and f(x). This will give you three linear equations in a, b, and c, which can be solved by any of the usual means for solving systems of linear equations.
Fortunately, this set of data includes the vertex of the function, making it easy to start with the vertex form:
f(x) = a(x -h)^2 +k
where (h, k) is the vertex (minimum, in this case), and "a" is the vertical scale factor. The value of "a" is easily determined as being the difference between f(h+1) and f(h). Here, h=0, so that is f(1) -f(0) = 3-2 = 1.
Answer:
x² +2
Step-by-step explanation:
A square orange rug has a green square in the center. The side length of the green square is x inches. The width of the orange band that surrounds the green square is 12 in. What is the area of the orange band?
Answer:
The area of the orange band is 576 + 48x square inches
Step-by-step explanation:
Step 1: Area of the green square
The area of the green square =[tex]side^2[/tex]
The area of the green square = [tex]x^2[/tex] square inches
Step 2: Area of the orange square
The area of the orange square =[tex]side^2[/tex]
The side of the orange square = 12+12 + x = 24 +x
Now the area of the orange square =[tex](x+24)^2[/tex]
Step 3: The area of the orange band
Area of the orange band = area of the orange square - area of the green square
Area of the orange band = [tex](x+24)^2 - x^2[/tex]
expanding and solving the equation we get
[tex]x^2 + 24^2 +48x - x^2[/tex]
[tex]576 + 48 x[/tex] square inches
Final answer:
The area of the orange band surrounding the central green square on the rug is found by subtracting the area of the green square from the area of the entire rug. The formula for the area of the orange band is 48x + 576 square inches, where x represents the side length of the green square.
Explanation:
To find the area of the orange band on the rug, we need to calculate the area of the entire rug and subtract the area of the central green square. The width of the orange band is given to be 12 inches. Therefore, each side of the orange rug is increased by 2 times 12 inches (for both the left and the right side of the green square), making the total length of the rug's side x + 2(12) inches.
The area of the entire rug, which is a larger square, is[tex](x + 24)^2[/tex] square inches. The area of the central green square is [tex]x^2[/tex]square inches. To find the area of the orange band, we subtract the area of the green square from the area of the entire rug which is: [tex](x + 24)^2 - x^2[/tex].
Expanding the squared term we get: [tex]x^2 + 48x + 576 - x^2[/tex], which simplifies to 48x + 576 square inches. That's the area of the orange band surrounding the green square.
15. The volume of a refrigerator is x3-3x2-16x-12. Its height is x + 2. What
are the other two dimensions?
A. x + 6 and x - 1
B. x-3 and x + 2
C. x-2 and x + 3
D. x-6 and x + 1
Final answer:
The volume of the refrigerator is factored by dividing with the given height, resulting in a quadratic polynomial that provides the other two dimensions. Upon factoring, we discover that the other dimensions are x - 6 and x + 1, corresponding to option D.
Explanation:
The volume of the refrigerator is given by the polynomial [tex]x^3 - 3x^2 - 16x - 12[/tex]. To find the other two dimensions of the refrigerator, we need to factor this polynomial using the given height of the refrigerator, which is x + 2. The goal is to divide the volume polynomial by the height polynomial to get the product of the remaining two dimensions.
We proceed with polynomial division or factoring:
Divide the volume polynomial by x + 2 using synthetic division or long division.
The result should be a quadratic polynomial that further factors into the product of two linear factors corresponding to the unknown dimensions.
Factor the quadratic polynomial to find the two missing dimensions.
In this case, the volume polynomial [tex]x^3 - 3x^2 - 16x - 12[/tex] can be divided by x + 2 to yield [tex]x^2 - 5x - 6[/tex], which can then be factored into (x - 6)(x + 1). Hence, the other two dimensions are x - 6 and x + 1, making option D correct.
A game designer must decide how to color five buildings that are in a row. Using only the colors yellow, green, red, and blue, each building must be painted with exactly one color. Any two neighboring buildings must be different colors, and the first, third, and fifth buildings must be different colors. How many ways are there to paint the five buildings?
Answer:
The total of ways the buildings can be painted are = 4 [tex]\times[/tex] 3 [tex]\times[/tex] 2 [tex]\times[/tex] 2 [tex]\times[/tex] 1 = 48 ways.
Step-by-step explanation:
i) color five buildings that are in a row.
ii) any two neighboring buildings must be different colors
iii) the first third and fifth buildings must be different colors.
iv) the number of ways to paint the fist building are 4.
v) the number of ways to paint the second building are 3.
vi) the number of ways to paint the third building are 2.
vii) the number of ways to paint the fourth building are 2.
viii) the number of ways to paint the last building are 1.
ix) therefore the total of ways the buildings can be painted are
= 4 [tex]\times[/tex] 3 [tex]\times[/tex] 2 [tex]\times[/tex] 2 [tex]\times[/tex] 1 = 48 ways.
Answer:
84
Step-by-step explanation:
we can split it into 2 cases: 1 case is when you choose the last building first and the second case is when you choose it last: so it is 4x2x2x3 for the first case and 4x3x3x1 for the last. So it’s 36+48=84 total cases.
The product of two numbers is a ______ of both numbers
Step-by-step explanation:
Given,
The product of two numbers = a
To find, the both numbers = ?
Let the two numbers = x
∴ x × x = a
⇒ [tex]x^{2}[/tex] = a
⇒ [tex]x^{2} =\sqrt{a}^2[/tex]
Comparing the powers, we get
⇒ x = [tex]\sqrt{a}[/tex]
∴ First number = [tex]\sqrt{a}[/tex] and Second number = [tex]\sqrt{a}[/tex]
Thus, the product of two numbers is a, [tex]\sqrt{a}[/tex] of both numbers.
4x-y=1 slope intercept form
Answer:
y=4x-1
Step-by-step explanation:
4x-y=1
4x=y+1 then negative Y becomes positive after going to the other side of the equal sign.
4x-1=y the positive 1 becomes negative after going to the other side of the equal sign.
Answer:
y = 4x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c
Given
4x - y = 1 ( subtract 4x from both sides )
- y = - 4x + 1 ( multiply through by - 1 )
y = 4x - 1 ← in slope- intercept form
(ab + 3)(ab - 3)
2262 +9
o alb2-6ab-9
o 2²2²-9
Answer:
a^2b^2 - 3ab + 3ab - 9
a^2b^2 - 9
Step-by-step explanation:
Solve by elimination -2x+2y=6 and 4x×2y=-5
Answer:
x=-11/6, y=7/6. (-11/6, 7/6).
Step-by-step explanation:
-2x+2y=6
4x+2y=-5
-----------------
2(-2x+2y)=2(6)
4x+2y=-5
----------------------
-4x+4y=12
4x+2y=-5
----------------
6y=7
y=7/6
4x+2(7/6)=-5
4x+14/6=-5
4x=-5-14/6
4x=-30/6-14/6
4x=-44/6
x=(-44/6)/4
x=(-44/6)(1/4)
x=-44/24
simplify
x=-11/6
Please answer !!!!!!!!!
Answer:
answer is b
Step-by-step explanation:
look at the picture
Yo sup??
slope=y2-y1/x2-x1
just take any value of x1 x2 y1 and y2
let x1,y1=2,1
and
x2,y2=4,-2
plugging in the values
slope=-2-1/4-2
=-3/2
therefore your answer is option 2
Hope this helps
Determine the measure of the missing angles. Show your work! Be ready to discuss your answer.
For a.
Since there are already two angles given for the triangle, we can measure the last angle using this formula:
90 + 55 + a = 180
Now solve for "a".
90 + 55 + a = 180
145 + a = 180
a = 180 - 145
a = 35°
For b.
From the picture above, the two triangle's tip are touching and having to form vertical angles. This means that the angles are congruent to each other.
Now that we have two angles in the second triangle(35 and 120), we can use the same formula:
35 + 120 + b = 180
Now solve for "b":
35 + 120 + b = 180
155 + b = 180
b = 180 - 155
b = 25°
Answer:
a = 35 b = 25
Step-by-step explanation:
Triangles always add up to 180 degrees. Knowing this we can first solve the triangle with the right angle.
55 + 90 + a = 180
Before we solve this, keep in mind that the reflective property will be used on angle a, giving the answer to the third angle in the second triangle.
145 + a = 180
-145 -145
a = 35
Now that we have a solved use the reflective property to get it on the second triangle.
120 + 35 + b = 180
155 + b = 180
-155 -155
b = 25
There you have your two angles.
Hope this helped you out.
What is the answer to 2(x+2)+2(x+4)=28 ?
Answer:
x=4
Step-by-step explanation:
2(x+2)+2(x+4)=28
Simplify the equation
2x+4+2x+8=28
4x+12=28
4x=16
x=4
GIVING BRAINLIEST Write a proportion that could be used to solve for each variable. Then solve. 16 walls in 40 hours 3 walls in h hours a. 16/40 = h/3; h = 1.2 c. 16/h = 3/40; h = 213.3 b. 16/40 = 3/h; h = 7.5 d. 16/40 = 3/h; h = 8.5
The proportion that could be used to solve for the variable is [tex]\frac{16}{40}=\frac{3}{h}[/tex] ; h = 7.5 ⇒ answer b
Step-by-step explanation:
A proportional relationship: one variable is always a constant value times the other, that constant is called the constant of proportionality
y = k x is the equation of the proportional relationshipWe can write the proportional relationship in the form [tex]\frac{y_{1}}{x_{1}}=\frac{y_{2}}{x_{2}}=k[/tex]The number of walls and the number of hours are increased or decreased together
∴ The number of walls and the number of hours are proportion
∵ 16 walls in 40 hours
∵ 3 walls in h hours
- By using the second rule above
∴ [tex]\frac{16}{40}=\frac{3}{h}[/tex]
The proportion that could be used to solve for the variable is [tex]\frac{16}{40}=\frac{3}{h}[/tex]
Let us solve it to find h
∵ [tex]\frac{16}{40}=\frac{3}{h}[/tex]
- By using cross multiplication
∴ 16 × h = 3 × 40
∴ 16 h = 120
- Divide both sides by 16
∴ h = 7.5
The value of h is 7.5 hours
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Question 4:
Gregory is x years old. Daisy is 2 years older than Gregory. The sum of their ages is 40.
(a) Form an equation in terms of x.
(b) Solve the equation and work out Gregory's and Daisy's ages.
gregory is 19 years old and daisy is 21 because 21 is two more that 19 but 19 +21=40
The correct answer is:
Gregory is 19 years old and daisy is 21
Applying linear equation
Let,
Age of Gregory = x years
Age of Daisy = (x+2) years
An equation in term of x
x + (x+2) = 40
2x + 2 = 40
2x = 40 - 2
x = [tex]\frac{38}{2}[/tex]
x = 19
∵ 19+21=40
⇒ Gregory is 19 years old
⇒ daisy is 21 years old
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Find the missing values of the variables
Answer:
What
Step-by-step explanation:
What is the missing variables
Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule
A(n) = 5+(n-1) (1/6)
Answer:
First term: 5
Fourth term: 5 1/2
Tenth term: 6 1/2
Step-by-step explanation:
Let's find the first, fourth and tenth terms of the arithmetic sequence described by the given rule:
A(n) = 5 + (n-1) (1/6)
First term:
A(1) = 5 + (1-1) (1/6)
A(1) = 5 + (0) (1/6)
A(1) = 5
Fourth term:
A(4) = 5 + (4-1) (1/6)
A(4) = 5 + (3) (1/6)
A(4) = 5 + 3/6 = 5 3/6 = 5 1/2 (simplifying)
Tenth term:
A(10) = 5 + (10-1) (1/6)
A(10) = 5 + (9) (1/6)
A (10) = 5 + 9/6 = 6 3/6 = 6 1/2 (simplifying)
if f(x)=3x-1 and g(x)= x+2, find (f-g)(x)
Answer:
Step-by-step explanation:
(f-g)(x) = f(x)- g(x)
= 3x - 1 - ( x + 2)
=3x - 1 - x - 2
= 2x - 3
Which of the following is equivalent to (7x + 3y)(8x + 5y)?
To find the product of (7x + 3y)(8x + 5y), you can use the distributive property of multiplication. The equivalent expression is 56x^2 + 59xy + 15y^2.
Explanation:To find the product of (7x + 3y)(8x + 5y), you can use the distributive property of multiplication over addition.
This means that each term in the first expression is multiplied by each term in the second expression.
Here are the steps:
Apply the distributive property to multiply 7x by each term in the second expression: 7x * 8x + 7x * 5y
Apply the distributive property to multiply 3y by each term in the second expression: 3y * 8x + 3y * 5y
Simplify each term: 56x^2 + 35xy + 24xy + 15y^2
Combine like terms: 56x^2 + 59xy + 15y^2
Therefore, the expression (7x + 3y)(8x + 5y) is equivalent to 56x^2 + 59xy + 15y^2.
In the question for exponential functions y=a•b^x how does the a term relate to a key feature of the graph
Answer:
es mi amigos senior le si nueve diez veite treinta Cien si onu fose locas
Step-by-step explanation:
Point A is located at (3,-6) and point A is located at (1-2). What is the scale factor?
Answer:
The scale factor is 3.
Step-by-step explanation:
Let the origin O(0,0) is the reference point and the coordinates of the point A are given by (3,-6).
Therefore, the distance OA is given by [tex]\sqrt{(3 - 0)^{2} + (- 6 - 0)^{2}} = 3\sqrt{5}[/tex] units.
Again, the coordinates of point A' are (1,-2).
Therefore, the distance OA' is given by [tex]\sqrt{(1 - 0)^{2} + (- 2 - 0)^{2}} = \sqrt{5}[/tex] units.
Hence, the scale factor is [tex]\frac{OA}{OA'} = \frac{3\sqrt{5} }{\sqrt{5}} = 3[/tex]. (Answer)
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(if your reading this I hope you have a great day!)
Write f(x)=8x^2-4x+11 in vertex form
Answer:
[tex]f(x)=8(x-\frac{1}{4})^{2}+\frac{21}{2}[/tex]
or
[tex]f(x)=8(x-0.25)^{2}+10.5[/tex]
Step-by-step explanation:
we have
[tex]f(x)=8x^{2}-4x+11[/tex]
This is a vertical parabola open upward (because the leading coefficient is positive)
The vertex is a minimum
Convert to vertex form
Factor the leading coefficient
[tex]f(x)=8(x^{2}-\frac{1}{2}x)+11[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]f(x)=8(x^{2}-\frac{1}{2}x+\frac{1}{16})+11-\frac{1}{2}[/tex]
[tex]f(x)=8(x^{2}-\frac{1}{2}x+\frac{1}{16})+\frac{21}{2}[/tex]
Rewrite as perfect squares
[tex]f(x)=8(x-\frac{1}{4})^{2}+\frac{21}{2}[/tex] ----> equation in vertex form
or
[tex]f(x)=8(x-0.25)^{2}+10.5[/tex]
The vertex is the point (0.25,10.5)
ΔDEF and ΔXYZ are similar isosceles triangles. What is the measure of X?
75°
105°
60°
30°
Answer: Angle X = 30
Step-by-step explanation: First and foremost, we should recognize that an isosceles triangle has two sides equal and the two angles subtended by the two equal sides are also equal in measurement.
This means. In the diagram on the left, line DE = line DF and that is 10cm.
The similar angles are the ones subtended by the lines identified as being equal, that is
Angle E = angle F and that is 75. If both angles measure a combined total of 150 the third angle can be derived simply as
180 - (75+ 75)
{Sum of angles in a triangle = 180}
180 - (150)
= 30
Therefore angle D = 30.
However having been given in the question that both triangles are similar and are isosceles, then
Angle D = Angle X and that is 30
Answer:
30 Good sir or miss sorry if I'm late dear
When solving the equation 2y2 – 16y = 6 by completing the square, what is your first step?
Question 6 options:
Divide –16 by 2 and square the result.
Divide each side of the equation by 2.
Take the square root of 6.
Subtract 6 from each side of the equation.
Answer:
Divide each side of the equation by 2.
Step-by-step explanation:
(I took the test so i know its right) Basically, when doing the this by completing the square we need y^2 by itself, so we divide 2y^2-16y=6 by two first.
Answer:
Divide each side of the equation by 2.
Step-by-step explanation:
2y² – 16y = 6
Divide both sides by 2
y² - 8y = 3
Which set of integers is NOT a Pythagorean triple and are NOT the side lengths of a right triangle?
A.) 12 ,16 ,20
B.)10 ,24 ,26
C.)14, 48, 50
D.)27, 32, 45
The set of integers 27, 32, 45 is NOT a Pythagorean triple and are NOT the side lengths of a right triangle ⇒ D
Step-by-step explanation:
The Pythagorean triple is:
The sum of the squares of the least two numbers is equal to the square of the greatest numbera, b and c are three integers where c is the greatest one,then if a² + b² = c², then a, b and c are Pythagorean triplePythagorean triple can form side lengths of a right triangleA. 12, 16, 20
∵ 20 is the greatest number
∵ (12)² + (16)² = 144 + 256 = 400
∵ (20)² = 400
∴ (20)² = (12)² + (16)²
∴ The set of integers 12, 16, 20 is a Pythagorean triple
∴ 12, 16, 20 are the side lengths of a right triangle
B. 10, 24, 26
∵ 26 is the greatest number
∵ (10)² + (24)² = 100 + 576 = 676
∵ (26)² = 676
∴ (26)² = (10)² + (24)²
∴ The set of integers 10, 24, 26 is a Pythagorean triple
∴ 10, 24, 26 are the side lengths of a right triangle
C. 14, 48, 50
∵ 50 is the greatest number
∵ (14)² + (48)² = 196 + 2304 = 2500
∵ (50)² = 2500
∴ (50)² = (14)² + (48)²
∴ The set of integers 14, 48, 50 is a Pythagorean triple
∴ 14, 48, 50 are the side lengths of a right triangle
D. 27, 32, 45
∵ 45 is the greatest number
∵ (27)² + (32)² = 729 + 1024 = 1753
∵ (45)² = 2025
∴ (45)² ≠ (27)² + (32)²
∴ The set of integers 27, 32, 45 is NOT a Pythagorean triple
∴ 27, 32, 45 are NOT the side lengths of a right triangle
The set of integers 27, 32, 45 is NOT a Pythagorean triple and are NOT the side lengths of a right triangle
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What is the answer plz help-thank you
Answer:
14.1cm (3s.f.)
Step-by-step explanation:
Please see attached picture for full solution.
sine angle= opp/hyp
cosine angle= adj/hyp