Question

a boat is anchored in the water. the anchor lies at point a. at low tide, the boat is floating 20 feet above the seafloor and is a horizontal distance of 40 feet away from its anchor. at high tide, the boat is a horizontal distance of 35 feet away from its anchor.
two right triangle diagrams: left labeled low tide with vertical leg 20 ft, horizontal leg 40 ft, right angle at bottom left, hypotenuse to point a; right labeled high tide with vertical leg ? ft, horizontal leg 35 ft, right angle at bottom left, hypotenuse to point a
approximately how high is the boat floating above the seafloor at high tide? assume the anchor rope remains tight, without any slack.
a. 15.6 ft
b. 27.8 ft
c. 35.7 ft
d. 22.5 ft

Explanation:

Step1: Calculate rope length at low tide

Use Pythagorean theorem: $c = \sqrt{20^2 + 40^2} = \sqrt{400 + 1600} = \sqrt{2000} \approx 44.72$ ft

Step2: Find height at high tide

Let height = $h$. Rope length same: $h = \sqrt{c^2 - 35^2} = \sqrt{2000 - 1225} = \sqrt{775} \approx 27.8$ ft

Answer:

B. 27.8 ft