A bird is perched on a tree branch that is 23 feet tall. The diagonal distance between you and the bird is 28 feet. You are 5.5 feet tall. Using the inverse of sine, what is the angle of elevation you use to look at the bird?(1 point)

Question

Responses

11°
11°

39°
39°

55°
55°

50°

Answer 1

To find the angle of elevation to the bird, we can use the inverse sine function. First, we need to determine the height difference between the bird and your eye level.

1. Height of the bird: 23 feet
2. Your height: 5.5 feet
3. Height difference: \( 23 - 5.5 = 17.5 \) feet

Next, we know the diagonal distance from you to the bird is 28 feet. We can now use the sine function:

\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{17.5}{28} \]

Calculating the sine value:

\[ \sin(\theta) = \frac{17.5}{28} \approx 0.625 \]

Now, use the inverse sine function to find the angle:

\[ \theta = \arcsin(0.625) \]

Calculating the angle:

\[ \theta \approx 39° \]

Therefore, the angle of elevation you use to look at the bird is 39°.