Question

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 formed is feet. 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 the short - leg length

The shorter leg of the right - triangle (vertical distance from Lisa's eye - level to the hoop) is \(8.5 - 5=3.5\) feet.

Step2: Recall angle relationship

The angle of depression from the hoop to Lisa is equal to the angle of elevation from Lisa's line of sight to the hoop due to the property of alternate interior angles.

Step3: Determine the trigonometric function

Since we know the lengths of the opposite (\(3.5\) feet) and adjacent (\(10\) feet) sides of the right - triangle, we use the tangent function (\(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\)).

Step4: Calculate the angle

We have \(\tan\theta=\frac{3.5}{10} = 0.35\). Then \(\theta=\arctan(0.35)\approx19^{\circ}\) (using a calculator to find the inverse - tangent).

Answer:

The length of the shortest leg of the right triangle that formed is \(3.5\) feet.
The angle of depression from the hoop to Lisa is equal to the angle of elevation from Lisa's line of sight to the hoop.
Because the lengths of the opposite and adjacent sides are known, use the tangent function.
The angle of depression, rounded to the nearest degree, is approximately \(19\) degrees.