Question

a surveyor 50 meters from the base of the cliff measures the angle of elevation to the top of the cliff at 72° what is the height of the cliff round to the nearest meter (use SOH-CAH-TOA)​ show work

Answer 1

The height of the cliff is
`154\ m`

Explanation:

Let

x-----> the angle of elevation

we know that

The tangent of angle x is equal to divide the opposite side angle x by the adjacent side angle x

In this problem

The opposite side angle x is the height of the cliff

The adjacent side angle x is the horizontal distance from the base of the cliff

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

we have

`x=72\°`

`O=h`

`A=50\ m`

substitute the values and solve for h

`tan(72\°)=(h)/(50)`

`h=(50)tan(72\°)=154\ m`