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.
To find the angle of elevation, we can use the inverse sine function. Let's denote the height of the rock feature as "h" and the diagonal distance as "d".
We are given that h = 300 feet and d = 750 feet.
The angle of elevation (θ) is the angle between the line of sight (from you to the rock feature) and the horizontal line.
Using the sine function, we have sin(θ) = h/d.
Taking the inverse sine (sin^(-1)) of both sides, we have θ = sin^(-1)(h/d).
Now, substituting the given values, we have θ ≈ sin^(-1)(300/750).
Calculating this, we find θ ≈ 24.3 degrees.
Rounding this to the nearest whole degree, the angle of elevation is approximately 24 degrees.