Arc Length Formula

Question

A 70 foot tall tree r feet from an observer subtends an angle of 1.75 degrees. Use the arc length formula to estimate r (the distance between the observer and the tree) to the nearest foot.

Answer 1

The arc formula: s=rθ, where s is approximately the tree height

r = s/θ, but θ needs to be in radians

θ = 1.75(π/180) ≈ 0.031

r =70/0.031 = 2291.83 feet

Note:

tan(θ) = 70/r

r=70/tan(1.75°) = 70/0.0355 = 2291.12 feet