Question

An aerial photograph is taken of a building. The photograph is made when the angle of elevation of the sun is 25 degrees. The shadow is determined to be 80 feet long. How tall is the building?

Answer 1

Using the tangent function with the given angle of elevation (25 degrees) and the shadow length (80 feet), the approximate height of the building is determined to be 37.304 feet.

Step-by-step explanation:

To determine the height of the building, we can use trigonometry, specifically the tangent function which relates the angles of a right triangle to the ratio of the opposite side over the adjacent side. Here, the angle of elevation is 25 degrees, and the length of the shadow is 80 feet.

Let's denote the height of the building as h. We can write the trigonometric equation as:

tan(25°) = h / 80 feet

To find h, we solve for it:

h = 80 feet * tan(25°)

Using a calculator, we find:

h = 80 feet * 0.4663 (approximate value of tan(25°))

h = 37.304 feet

Therefore, the height of the building is approximately 37.304 feet.

Answer 2

37.3 ft

Step-by-step explanation:

SOH CAH TOA reminds you that ...

Tan = Opposite/Adjacent

In this geometry, the side adjacent to the angle is the 80 ft shadow, and the opposite side is the height of the building. Then we have ...

tan(25°) = height/(80 ft)

(80 ft)·tan(25°) = height ≈ 37.3 ft