Question

From the top of a cliff 40 feet high, the angle of depression to an object in the riverbelow is 32 degrees. How far away from the base of the cliff is the object?

Answer 1

Finding how far is an object

We know that:

- The top of the cliff is 40 feet high

- The angle of depression to an object is 32 degrees

We want to find how far is the object from the base, let's call that distance X

We know that

Alternate Interior Angles:

when two parallel lines are crossed by a transversal line the angles of the sides of the transversal are equal

If we simplify the first drawing we have that

Tangent of an angle

We know that

$\begin{gathered} \tan (32º)=\frac{40ft}{x} \\ \tan (32º)=0.625 \\ 0.625=\frac{40ft}{x} \end{gathered}$

Now we can find x:

$\begin{gathered} x=\frac{40ft}{0.625} \\ x=64ft \end{gathered}$

Answer: the object is 64ft far from the base of the cliff