Question

A flagpole is 25 ft tall. The flagpole is casting a shadow that is 42 feetlong. What is the angle of depression?

Answer 1

We can draw the following picture:

then we need to find angle theta. However, in order to find theta, we must find angle x first.

Since we have a right triangle, we can apply the tangent function as:

`\tan x=(42)/(25)`

then, x is given by

`\begin{gathered} x=\tan ^(-1)((42)/(25)) \\ x=\tan ^(-1)(1.68) \end{gathered}`

then, x is equal to

`x=59.24\text{ degr}ees`

Now, angle x and angle theta are complementary, this means that

`x+\theta=90`

then, we have

`\begin{gathered} \theta=90-x \\ \theta=90-59.24 \\ \theta=30.76 \end{gathered}`

Therefore, the angle of depression (theta) is equal to 30.76 degrees.