Question

The length of the shadow of a building is 90 meters as shown below.

30°
Shadow
90 m

Building
A B
What is the height of the building to the nearest meter?
180 m
52 m
156 m
60 m

Answer 1

156 m

Explanation:

We can use the 30°-60°-90° triangle theorem, and figure out that the side lengths of the triangle need to be in a 1:
`√(3)`: 2 ratio. The 1 is the shorter leg,
`√(3)` is the longer leg, and the 2 is the hypotenuse.

In this case, we are given the shorter leg, and are asked to find the longer leg. Since the length of the shorter leg is 90 m, we can multiply that by
`√(3)`. This gives us approximately 156 m.