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

39°
39°

11°
11°

55°
55°

50°

Answer 1

To find the angle of elevation to the bird, we can use the definition of the sine function in a right triangle.

1. First, determine the height difference between you and the bird. The bird is perched 23 feet high, and you are 5.5 feet tall: \[ \text{Height difference} = 23, \text{feet} - 5.5, \text{feet} = 17.5, \text{feet} \]

2. Next, we have the diagonal distance to the bird (the hypotenuse) as 28 feet. The angle of elevation \( \theta \) can be calculated using the sine function: \[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{17.5, \text{feet}}{28, \text{feet}} \]

3. Now, calculating \( \sin(\theta) \): \[ \sin(\theta) = \frac{17.5}{28} \approx 0.625 \]

4. To find the angle \( \theta \), use the inverse sine function: \[ \theta = \sin^{-1}(0.625) \]

5. Now, calculating \( \theta \): \[ \theta \approx 39° \]

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