Question

solving for angle measures of right triangles
determining an angle of depression
use the diagram and complete the steps to find the measure of the angle of depression from the top of the hoop to lisa.
the length of the shortest leg of the right triangle that is formed is 3.5 feet.
the angle of depression from the hoop to lisa is dropdown to the angle of elevation from lisa’s line of sight. options: complementary, congruent, supplementary.
because the lengths of the opposite and adjacent sides use the dropdown function.

Explanation:

Step1: Find the vertical leg length

The total vertical height is 8.5 ft, and Lisa's height is 5 ft. So the vertical leg of the right triangle is \( 8.5 - 5 = 3.5 \) ft (this matches the given shortest leg). The horizontal leg is 10 ft.

Step2: Analyze angle relationship

The angle of depression and the angle of elevation are alternate interior angles (since the horizontal lines are parallel), so they are congruent.

Step3: Determine the trigonometric function

We have the opposite side (3.5 ft) and adjacent side (10 ft) to the angle of elevation (which is congruent to the angle of depression). The tangent function is \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \), so we use the tangent function.

Answer:

• The angle of depression from the hoop to Lisa is congruent to the angle of elevation from Lisa’s line of sight.
• Because the lengths of the opposite and adjacent are known, use the tangent function.