A bridge builder wants to know the width of a river. He stands at point A along the river. He picks a point C directly across the river. He then walks downstream 90 feet from point A to point B. From point B, he sites C and determines the angle between the bank and point C (θ), to be 43º. What is the width of the river?

To find the length of the new roofline, we can use the tangent function. The length is approximately 26.9 feet.

To find the length of the new roofline, we can use the trigonometric function tangent. Let's call the length of the new roofline 'x'. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the roofline, which is 32 feet, and the adjacent side is the horizontal distance, which is 'x' feet. So, we can set up the equation:

tan(50°) = 32/x

To solve for 'x', we can multiply both sides of the equation by 'x' and then divide both sides by tan(50°). This gives us:

x = 32/tan(50°)

Using a calculator, we can find that tan(50°) ≈ 1.1917. So, substituting this value into the equation, we get:

x ≈ 32/1.1917

By calculating this, we find that the length of the new roofline is approximately 26.9 feet.

c:

 to find x multiply the side (24) by the tangent of the angle(13)

 so 24 * tan(13) = 5.5408

D:

 to find x

 divide the side (10) by the sin of the angle (20)

10/sin(20) = 29.238

 Round the answers as needed.

28.7251 =

 28 degrees

 then take the decimal and multiply by 60 to get the minutes

 so 0.7251 *60 = 43.506, use the whole number (43)

 so now you have 28 degrees, 43 minutes

 now take the remaining decimal ( 0.506) and multiply by 60

0.506*60= 30.36

 when you have a decimal left over for the seconds, keep that as is.

 so you now have 28 degrees, 43 minutes and 30.36 seconds

 use ' for minutes and " for seconds

28 degrees 43' 30.36"

Final answer:

To convert 28.7251 degrees to degrees, minutes, and seconds, take the whole number of degrees (28) and multiply the decimals (.7251) by 60 to get the minutes (43). Then multiply the remaining decimal of the minutes (.506) by 60 to get the seconds (30), resulting in 28 degrees, 43 minutes, and 30 seconds (28° 43' 30").

Explanation:

To convert 28.7251 degrees to degrees, minutes, and seconds, you follow a multi-step process which involves converting the decimal part of the degrees into minutes and then into seconds. First, identify the whole number of degrees, which is 28 in this case.

To convert the decimal part (.7251) to minutes, multiply by 60. Using the operation provided in the reference, with 0.7251 × 60, you get 43.506 minutes. The whole number part, 43, is the minutes.

To convert the remaining decimal part of minutes (.506) into seconds, again multiply by 60. This gives you (.506  imes 60) 30.36 seconds, which when rounded to the nearest second is 30 seconds.

Therefore, 28.7251 degrees is equal to 28 degrees, 43 minutes and 30 seconds (28° 43' 30").

Answer:

Option B is correct.

Step-by-step explanation:

We have been given x-axis representing quantity

And y-axis representing price

S1 and S2 are supply

So, these two supply have parallel lines which means they will never intersect they will remain same throughout the domain.

Therefore, the supply stayed the same.

Option B is correct.

Answer: The number of miles per hour he averages on his way home is 36 mph.

Step-by-step explanation:

Since we have given that

Distance traveled by Rosario = 60 miles

Time taken for road trip = 2.75 hours

Speed at which he on his way to the rink = 55 mph

Let X be the speed at which he averages on his way home.

So, According to question, we get that,

[tex]\dfrac{60}{55}+\dfrac{60}{x}=2.75\\\\1.09+\dfrac{60}{x}=2.75\\\\\dfrac{60}{x}=2.75-1.09\\\\\dfrac{60}{x}=1.659\\\\x=\dfrac{60}{1.659}\\\\x=36.16\\\\x=36\ mph[/tex]

Hence, the number of miles per hour he averages on his way home is 36 mph.

Answer:

y=21.5x+10.5

Step-by-step explanation:

Rounded to the nearest meter, the height of the plane is approximately 405 meters.

So, the correct answer is B. 405 m.

To find the height of the plane, we can use trigonometry, specifically the tangent function.

Let's denote the height of the plane as h (in meters).

From the information given, we know that the angle of depression from the airplane to the atoll is 5 degrees, and the horizontal distance from the airplane to the atoll is 4629 meters.

Using the tangent function, we have:

tan(angle of depression) = height / horizontal distance

tan(5 degrees) = h / 4629

To find the value of h, we can rearrange the equation:

h = 4629 * tan(5 degrees)

Now, let's calculate the height of the plane:

h ≈ 4629 * 0.0874886635 ≈ 404.773 meters

Rounded to the nearest meter, the height of the plane is approximately 405 meters.

So, the correct answer is B. 405 m.

To learn more trigonometry click:

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Answer:

9.2

Step-by-step explanation:

We are given that a figure in which a tangent and a secant to the circle.

We have to find the value of x.

Length of tangent segment=x

Length of secant segment=12 +5=17 units

Length of external segment=5 units

We know that secant-tangent theorem

It states that product of length of secant segment and its external segment is equal to square of length of tangent segment.

[tex]x^2=17\times 5=85 [/tex]

[tex]x=\sqrt{85}=9.2 units[/tex]

Hence, the value of x=9.2

45/10= 36/x

cross multiply

360/45X

360/45 = 8

the length is 8 meters

Answer:

the correct answer is A. 1/2 x 14 x 57

Step-by-step explanation:

i got it right on my test

The equation of the sphere with center (-3, 2, 9) and radius 6 is (x + 3)² + (y - 2)² + (z - 9)² = 6². The intersection of this sphere with the yz-plane is described by the equation (y - 2)² + (z - 9)² = 27.

The equation of a sphere with center (-3, 2, 9) and radius 6 is given by:

(x + 3)² + (y - 2)²+ (z - 9)² = 6²

To find the intersection of this sphere with the yz-plane, we need to set x = 0 in the equation:

(0 + 3)² + (y - 2)² + (z - 9)² = 6²

Simplifying this equation gives:

(y - 2)² + (z - 9)² = 27

So, the intersection of the sphere with the yz-plane is described by the equation (y - 2)² + (z - 9)² = 27.