Question

A bird is perched on a light pole that is 13 feet tall. You spot the bird as you’re walking across the street. If you are 5 feet tall, and the diagonal distance from you to the bird is 10 feet, what is the angle of elevation you are using to look at the bird? Use the inverse of sine to find your answer and round to the nearest whole degree.(1 point)

Answer 1

To find the angle of elevation to the bird, we can first determine the height difference between you and the bird and then use the sine function.

1. **Height of the bird**: 13 feet
2. **Height of the observer (you)**: 5 feet
3. **Height difference**: \( 13 - 5 = 8 \) feet

4. **Diagonal distance from you to the bird**: 10 feet

Now, we can use the sine function to find the angle of elevation \( \theta \):

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{\text{height difference}}{\text{diagonal distance}}
\]

In our case, the opposite side is the height difference (8 feet) and the hypotenuse is the diagonal distance (10 feet):

\[
\sin(\theta) = \frac{8}{10} = 0.8
\]

Now to find the angle \( \theta \), we can use the inverse sine function:

\[
\theta = \sin^{-1}(0.8)
\]

Using a calculator, we can find:

\[
\theta \approx 53.13^\circ
\]

Rounding to the nearest whole degree gives:

\[
\theta \approx 53^\circ
\]

Thus, the angle of elevation you are using to look at the bird is approximately **53 degrees**.