a building cast a shadow approximately 130 ft long on the street when the suns ray form an 82.9 degree angle with the earth. how tall is the building?

180-82.9-90= 7.1 degree
tan 7.1 = x/130ft
x= 16.19ft
is this correct? thanks!

x/130 = tan 82.9

x = 1043.70

reread the problem carefully. You have the angles switched. 82.9 degrees is almost overhead, so a tall building casts a relatively short shadow.

To find the height of the building, you are correct in using the tangent function. However, you made a small error in your calculations.

The correct calculations are as follows:

Let H be the height of the building.

tan(82.9 degrees) = H / 130ft

Rearranging the equation to solve for H:

H = 130ft * tan(82.9 degrees)

H = 491.73ft

Therefore, the height of the building is approximately 491.73 feet.

To find the height of the building, you can use basic trigonometry with the given information. Here's the step-by-step explanation:

1. Draw a diagram: Draw a diagram where you have a right triangle with the building as the vertical side, the shadow of the building as the horizontal side, and the sun's rays as the hypotenuse.

2. Identify the relevant angle: Identify the angle between the sun's rays and the ground. In this case, it is given as 82.9 degrees.

3. Determine the complement angle: Since the angle between the sun's rays and the ground is given, you can find the complementary angle by subtracting it from 90 degrees. In this case, it would be 90 degrees - 82.9 degrees = 7.1 degrees.

4. Use the tangent function: The tangent function (tan) relates the angle to the ratio of the lengths of the sides of a right triangle. In this case, you need to find the height (opposite side) in relation to the length of the shadow (adjacent side).

tan(7.1 degrees) = height/130 ft

Rearrange the equation to solve for the height:

height = tan(7.1 degrees) * 130 ft

5. Calculate the height: Use a calculator to find the value of the tangent of 7.1 degrees, and then multiply it by 130 ft to get the height of the building.

height ≈ tan(7.1 degrees) * 130 ft
height ≈ 0.1234 * 130 ft
height ≈ 16.04 ft (rounded to two decimal places)

So, based on the calculations, the height of the building is approximately 16.04 ft. Therefore, your answer of 16.19 ft is very close and may be due to rounding differences.