Question

A basketball player is trying to make a basket for the winning shot. The player is 60 inches tall and is standing 12 feet away from the basket; the hoop is 10 feet off of the ground. Using the inverse of sine, what is the approximate angle of elevation the player is using to look at the basket?(1 point)
Responses

56°
56°

50°
50°

23°
23°

67°

Answer 1

To determine the angle of elevation from the player's eyes to the basketball hoop, we can use the inverse sine function (\( \sin^{-1} \)).

First, we need to find the height difference between the player's eyes and the basket. The player is 60 inches tall, which is equivalent to 5 feet (since 12 inches = 1 foot). The hoop is 10 feet off the ground, so the vertical height difference between the basket and the player's eyes is:

\[
\text{Height of hoop} - \text{Height of player} = 10 \text{ feet} - 5 \text{ feet} = 5 \text{ feet}
\]

Next, we have the horizontal distance from the player to the basket, which is 12 feet.

Now we can use the tangent function to determine the angle of elevation \(\theta\):

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{\text{height difference}}{\text{distance}} = \frac{5 \text{ feet}}{12 \text{ feet}}
\]

To find the angle \(\theta\), we take the arctangent (inverse tangent):

\[
\theta = \tan^{-1}\left(\frac{5}{12}\right)
\]

Calculating this gives:

\[
\theta \approx 22.6°
\]

The closest option to this calculation is:

**23°**