Question

A man wants to determine the height of the lighthouse. he measured the angle at A and found that tan A = 3/4. What is the height of the lighthouse if A is 40 m from the base?

Answer 1

The height of the lighthouse is of 30m.

Explanation:

This situation can be represented by a right triangle.

The tangent of the angle is 3/4.

The tangent in a right triangle is given by the opposite side divided by the adjacent side.

What is the height of the lighthouse if A is 40 m from the base?

The height of the light house is the opposite side, which we want to find.

The distance is the adjacent side, which we have that is 40. So

`tan(A) = (x)/(40)`

`(3)/(4) = (x)/(40)`

`4x = 40*3`

`4x = 120`

`x = (120)/(4)`

`x = 30`

The height of the lighthouse is of 30m.