Answer:
The height of the cliff is [tex]154\ m[/tex]
Step-by-step 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
[tex]tan(x)=\frac{O}{A}[/tex]
we have
[tex]x=72\°[/tex]
[tex]O=h[/tex]
[tex]A=50\ m[/tex]
substitute the values and solve for h
[tex]tan(72\°)=\frac{h}{50}[/tex]
[tex]h=(50)tan(72\°)=154\ m[/tex]
