Question

find the angle of elevation from point c to point a.
(diagram: right triangle with right angle at b, a at top, b at bottom left, c at bottom right; ab = 5 mi, angle at a is 66°, angle at c is marked with ?)
angle of elevation = ? °

Explanation:

Step1: Recall triangle angle sum property

In a right - triangle \(ABC\) (right - angled at \(B\)), the sum of the interior angles of a triangle is \(180^{\circ}\). So we know that \(\angle A+\angle B+\angle C = 180^{\circ}\). Since \(\angle B = 90^{\circ}\) and \(\angle A=66^{\circ}\), we can find \(\angle C\) (the angle of elevation) by rearranging the formula.

Step2: Calculate the angle of elevation

We know that \(\angle C=180^{\circ}-\angle A - \angle B\). Substituting \(\angle A = 66^{\circ}\) and \(\angle B = 90^{\circ}\) into the formula, we get \(\angle C=180^{\circ}-90^{\circ}-66^{\circ}\). First, \(180 - 90=90\), then \(90 - 66 = 24\). So \(\angle C = 24^{\circ}\).

Answer:

\(24\)