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?

Question

asked Feb 27, 2023 536 views

1 Answer

Realkes · Answer 1 · 2023-03-03T08:10:22+0000

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:

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

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