Question

Find the angle of depression

Answer 1

Given:

In triangle ABC, $m\angle A=66^\circ, AB=5\text{ mi}$.

To find:

The angle of depression from point A to point C.

Solution:

According to angle sum property, the sum of all interior angles of a triangle is 180 degrees.

In triangle ABC,

$m\angle A+m\angle B+m\angle C=180^\circ$

$66^\circ+90^\circ+m\angle C=180^\circ$

$156^\circ+m\angle C=180^\circ$

$m\angle C=180^\circ-156^\circ$

$m\angle C=24^\circ$

We know that if a transversal line intersect the two parallel lines, then alternate interior angles are equal. So, the angle of depression from point A to point C is equal to the measure of angle C in triangle ABC.

Therefore, the angle of depression is 24 degrees.