Question

How far from the foot of a pole 26 meters high, must a 2 meter person stand so that the angle of elevation of the top of the pole is 10 degrees?

Answer 1

Let's draw an image to represent this question:

Then, in order to calculate the value of x, we can use the tangent relation of the 10° angle.

The tangent relation is given by the length of the opposite side to the angle over the length of the adjacent leg to the angle.

So we have:

$\begin{gathered} \tan (10\degree)=\frac{24}{x} \\ 0.176327=\frac{24}{x} \\ x=\frac{24}{0.176327} \\ x=136.11 \end{gathered}$

So the horizontal distance from the person to the pole is 136.11 meters.