Question

the angle of depression from top of a flag pole to a point on the ground is 30 digress if the point on the point on the ground is 75 feet from the base of the flag pole. A,how tall is the pole?B:find the diagonall distance

Answer 1

Let's make a diagram to represent this situation

As you can observe in the diagram, we have a right triangle, and we know one leg and one acute angle. So, in order to find the height y, we have to use the tangent function which relates the opposite leg and the adjacent leg.

$\begin{gathered} \tan 30=\frac{75}{y} \\ y=\frac{75}{\tan 30} \\ y\approx129.9 \end{gathered}$

Hence, the height of the pole is 129.9 feet, approximately.

To find the diagonal distance, we use the sine function which relates the opposite leg and the hypothenuse.

$\begin{gathered} \sin 30=\frac{75}{h} \\ h=\frac{75}{\sin 30} \\ h=\frac{75}{0.5}=150 \end{gathered}$

Hence, the diagonal distance is 150 feet.