Question

A bird is perched on the top of a building that is 13 feet tall. You spot the bird as you’re walking across the street. If you are 6 feet tall and the diagonal distance from you to the bird is 26 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 from your eyes to the bird, we first need to calculate the height difference between your eye level and the bird.

1. The height of the building is 13 feet.
2. Your height is 6 feet.
3. The height difference (h) between you and the bird is:
\[
h = \text{Height of building} - \text{Your height} = 13 \text{ ft} - 6 \text{ ft} = 7 \text{ ft}
\]

Now, you have a right triangle formed where:
- The vertical side (opposite side) is the height difference \( h = 7 \) ft.
- The diagonal (hypotenuse) is the distance from you to the bird, which is 26 ft.

To find the angle of elevation \( \theta \), we can use the sine function:
\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{h}{\text{hypotenuse}} = \frac{7}{26}
\]

Next, we take the inverse sine (arcsin) to find \( \theta \):
\[
\theta = \arcsin\left(\frac{7}{26}\right)
\]

Calculating \( \frac{7}{26} \):
\[
\frac{7}{26} \approx 0.2692
\]

Now, using a calculator:
\[
\theta = \arcsin(0.2692) \approx 15.7^\circ
\]

Rounding to the nearest whole degree:
\[
\theta \approx 16^\circ
\]

Thus, the angle of elevation you are using to look at the bird is approximately **16 degrees**.