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.
To find the angle of elevation, we need to use the inverse of sine. The angle of elevation, in this case, is the angle between your line of sight and the horizontal line.
We can use the right triangle formed between you, the bird, and the light pole to solve for the angle of elevation.
Let's label the right triangle as follows:
- The opposite side is the height of the light pole: 13 feet.
- The adjacent side is your height: 5 feet.
- The hypotenuse is the diagonal distance from you to the bird: 10 feet.
Using the sine function, we can write:
sin(angle of elevation) = opposite/hypotenuse
sin(angle of elevation) = 13/10
To find the angle of elevation, we need to take the inverse sine (sin^-1) of 13/10.
angle of elevation = sin^-1(13/10)
Using a calculator, we find:
angle of elevation ≈ 54.74 degrees
Rounding to the nearest whole degree, the angle of elevation is approximately 55 degrees.