The angle of elevation e from A to B and the angle of depression d from B to A are given. Find the measure of each angle.I need help with problem number 20.

Question

asked Sep 25, 2023 1.0k views

1 Answer

Ivor · Answer 1 · 2023-09-29T09:48:57+0000

Let AB represent the height of an airplane flying.

As:

$\begin{gathered} 1mile=5280feet \\ \therefore50miles=50*5280=264000feet \end{gathered}$

Using tangent of angles to solve for the measure of angles

$tan\theta=(Perpendicular)/(Base)$

where,

$\begin{gathered} Perpendicular=1000ft \\ Base=264000ft \end{gathered}$

Simplify

$\begin{gathered} tan\theta=0.037 \\ \theta=\tan^(-1)(0.037)=2.12^0\approx2^0(nearest\text{ degree\rparen} \end{gathered}$

Hence, the answer is

$\theta=2^0$