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.
Let x be the angle of elevation.
We can set up a right triangle with the height of the light pole (13 feet), the distance from you to the light pole (5 feet), and the diagonal distance from you to the bird (10 feet).
Using the sine function, we can set up the following equation:
sin(x) = opposite/hypotenuse
sin(x) = 13/10
To find x, we take the inverse sine of both sides:
x = arcsin(0.13)
Using a calculator, we find that the arcsin of 0.13 is approximately 7.461 degrees.
Therefore, the angle of elevation you are using to look at the bird is approximately 7 degrees.