Question

: Kareem wants to know how tall a building in his neighborhood is. Since he can't directly

measure the height of the building he decides to use the properties of right triangles. He walks 100
feet from the base of the building and looks up to the top. He estimates the angle from his vantage
point to the top of the building to be 75 degrees. About how tall is the building? Round your answer
to the nearest foot.

Answer 1

To solve this problem, we can use trigonometry and the properties of right triangles. We know that Kareem is standing 100 feet from the base of the building, and he estimates the angle from his vantage point to the top of the building to be 75 degrees. Let's call the height of the building "h".

Using tangent, we can set up the following equation:

tan(75) = h/100

Solving for h, we get:

h = 100 * tan(75)

Using a calculator, we get:

h ≈ 466 feet

Therefore, the building is about 466 feet tall, rounded to the nearest foot.