Question

solving for angle measures of right triangles
determining an angle of depression
diagram: basketball hoop, vertical dashed line (8.5 ft), horizontal dashed line, lisa (5 ft tall) with horizontal distance 10 ft from hoop base
3.5 feet
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.
because the lengths of the opposite and adjacent sides are known,
use the inverse tangent function.
the angle of depression, rounded to the nearest degree, is approximately blank degrees.

Explanation:

Step1: Find the opposite side length

The vertical distance between the hoop and Lisa's line of sight is \( 8.5 - 5 = 3.5 \) feet. This is the opposite side relative to the angle of depression (or elevation). The adjacent side is 10 feet (horizontal distance).

Step2: Use the arctangent function

The tangent of an angle \( \theta \) in a right triangle is \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). So, \( \tan(\theta)=\frac{3.5}{10} = 0.35 \). To find \( \theta \), we use the inverse tangent (arctangent) function: \( \theta=\arctan(0.35) \).

Step3: Calculate the angle

Using a calculator, \( \arctan(0.35)\approx19.29^\circ \), which rounds to 19 degrees.

Answer:

19