Question

A bird is perched on the top of a building that is 10 feet tall. You spot the bird as you’re walking across the street. If 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? Round to the nearest whole degree.(1 point)

Answer 1

To find the angle of elevation to the bird perched on top of a 10-foot tall building when the diagonal distance from you to the bird is 26 feet, we can use trigonometry.

We can set up a right triangle where:
- The height of the building is the opposite side (10 feet).
- The diagonal distance to the bird is the hypotenuse (26 feet).
- We need to find the angle of elevation (\(\theta\)), which is the angle between the horizontal line from you to the base of the building and your line of sight to the bird.

We use the sine function, which relates the opposite side to the hypotenuse:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{10}{26}
\]

Calculating \(\frac{10}{26}\):

\[
\frac{10}{26} = \frac{5}{13} \approx 0.3846
\]

Now we find the angle \(\theta\) by taking the arcsine:

\[
\theta = \arcsin(0.3846)
\]

Using a calculator:

\[
\theta \approx 22.5^\circ
\]

Rounding to the nearest whole degree gives:

\[
\theta \approx 23^\circ
\]

Thus, the angle of elevation is approximately **23 degrees**.