Question

A hawk is flying 130 meters up in the sky and spots a rodent on the ground at a 20

degree angle of depression. To the nearest meter, what is the horizontal distance
between the hawk and the rodent?

Answer 1

arc length d = ∫ √(1 + (dy/dx)²) dx

y = 228 - x²/57

dy/dx = -2x / 57

(dy/dx)² = (2x/57)²

Upper limit for integration:

y = 0 = 228 - x²/57

yields x = 114

d = ∫ √(1 + (2x/57)²) dx for 0 ≤ x ≤ 114 = 264.9 m

Explanation: