Question

a boy sitting on a platform 7.5m high he observes that the angle of elevation of the top of the opposite building is 40°.the platform is 37.5m away from the building .find the height of the building ​

Answer 1

The building is approximately 39 m high.

Explanation:

As seen in the diagram attached, a triangle can be formed between the boy, the top of the building, and the lateral distance between the boy and the building.

We can now use trigonometric laws to find the distance AC between the boy's head and the top of the building.

tan 40 = AC/37.5

AC = 37.5 X tan 40 = 31.46m

We have just obtained the distance from the boy's head to the building top.

To get the true height of the building, we have to add the height of the platform the boy is standing on to the value just found.

7.5m + 31.46m = 39m