You're hiking in Zion National Park when you stop to look at a specific rock feature. The rock feature is 300 feet above the base of the mountain, and the diagonal distance between you and the rock feature is 750 feet. Using the inverse of sine, what is the angle of elevation you are using to look up at the feature? Round your answer to the nearest whole degree.

Question

You're hiking in Zion National Park when you stop to look at a specific rock feature. The rock feature is 300 feet above the base of the mountain, and the diagonal distance between you and the rock feature is 750 feet. Using the inverse of sine, what is the angle of elevation you are using to look up at the feature? Round your answer to the nearest whole degree.

Answer 1

To find the angle of elevation, we can use the inverse sine function (also known as arcsine).

Let θ be the angle of elevation.

We are given that the opposite side of the triangle is 300 feet (the height of the rock feature) and the hypotenuse is 750 feet (the diagonal distance between you and the rock feature).

Using the sine ratio, we have:

sin(θ) = opposite/hypotenuse
sin(θ) = 300/750
sin(θ) = 0.4

Now, we can use the inverse sine function to find θ:

θ = arcsin(0.4)
θ ≈ 23.6 degrees

Therefore, the angle of elevation you are using to look up at the rock feature is approximately 24 degrees (rounded to the nearest whole degree).