Question

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)
Responses

50°50 degrees

39°39 degrees

55°55 degrees

11°

Answer 1

To find the angle of elevation from your eyes to the bird, we can use the inverse sine function (arcsin).

First, we need to find the height difference between the bird and your eyes. Since you are 5.5 feet tall and the bird is perched 23 feet up, the height difference is:

\[
\text{Height of the bird} - \text{Your height} = 23\, \text{feet} - 5.5\, \text{feet} = 17.5\, \text{feet}
\]

Next, we can use the relationship in a right triangle to find the angle of elevation. The height difference is the opposite side, and the diagonal distance (the hypotenuse) is 28 feet. The sine of the angle \(\theta\) can be expressed as:

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

Calculating that gives:

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

Now, we can find \(\theta\) using the inverse sine function:

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

Using a calculator:

\[
\theta \approx 38.68\, \text{degrees}
\]

Rounding it, the angle of elevation is approximately \(39^\circ\).

Therefore, the answer is:

**39°**