Question

A scuba diver has a taut rope connecting the dive boat to an anchor on the ocean floor. The rope is 95 feet long and the water is 40 feet deep. To the nearest tenth of a foot, how far is the anchor from a point directly below the boat? 103.1 ft 3,712.5 ft 86.2 ft 7,425 ft

Answer 1

AB = length of the rope = L = 95 ft

AC = depth of water = h = 40 ft

BC = distance of the anchor from a point directly below the boat = x

consider triangle ABC

using Pythagorean theorem , we get

AB² = AC² + BC²

L² = h² + x²

inserting the values

(95)² = (40)² +  x²

9025 = 1600 +  x²

subtracting 1600 both side

9025 - 1600 = 1600 - 1600 +  x²

x² = 7425

taking square root both side

x = sqrt(7425)

x = 86.2 ft