Question

etermining an angle
complementary
congruent
supplementary
the angle of depression from the hoop to lisa is
to the angle of elevation from lisas line of sight to the hoop.
because the lengths of the opposite and adjacent sides are known, use the
function.
the angle of depression, rounded to the nearest degree, is approximately
degrees.
8.5 ft
5 ft
10 ft

Explanation:

Step1: Identify angle - relationship

The angle of depression from the hoop to Lisa is congruent to the angle of elevation from Lisa's line of sight to the hoop. This is because of the property of alternate - interior angles formed by parallel horizontal lines.

Step2: Determine trigonometric function

We know the length of the opposite side ($8.5 - 5=3.5$ ft) and the adjacent side ($10$ ft) of the right - triangle formed. We use the tangent function since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step3: Calculate the angle

Let $\theta$ be the angle of depression. $\tan\theta=\frac{8.5 - 5}{10}=\frac{3.5}{10}=0.35$. Then $\theta=\arctan(0.35)$. Using a calculator, $\theta\approx19^{\circ}$.

Answer:

congruent; tangent; 19