Question

You are standing 143 feet away from the base of a building and your clinometer measures 17° when it’s looking at the top of the building. (This angle is the one between the ground and the top of the building). Please calculate the height of the building.

Answer 1

The height of the building is 43.7 feet.

Explanation:

Attached is a sketch of the problem.

We can use SOH CAH TOA to find our answer.

In this acronym, O is the opposite side, A is the adjacent side, and H is the hypotenuse. S is for the SIN function. C is for the COS function. T is for the TAN function.

We can calculate the height of the building by using the TAN function.

So we can say the tangent of angle x is the opposite side divided by the adjacent side.

`tan(x)=(O)/(A)`

Lets solve for
`O`.

Multiply both sides by
`A`.

`tan(x)*A=(O)/(A)*A`

Simplify the right side by cancelling the common factor of
`A`.

`tan(x)*A=O\\O=A*tan(x)`

Now lets evaluate the height of the building.

In this example we are given

`x=17\\A=143`

`O=143*tan(17)`

`O=43.7195`