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)=(40ft)/(x) \\ \tan (32º)=0.625 \\ 0.625=(40ft)/(x) \end{gathered}`

Now we can find x:

`\begin{gathered} x=(40ft)/(0.625) \\ x=64ft \end{gathered}`

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