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. low tide high tide 20 ft ? ft a a 40 ft 35 ft 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. 22.5 ft c. 27.8 ft d. 35.7 ft

Explanation:

Step1: Calculate the length of the anchor rope at low tide

Use the Pythagorean theorem \(c = \sqrt{a^{2}+b^{2}}\), where \(a = 20\) and \(b = 40\).

$$c=\sqrt{20^{2}+40^{2}}=\sqrt{400 + 1600}=\sqrt{2000}=20\sqrt{5}\approx44.72$$

Step2: Calculate the height of the boat at high tide

Let the height at high tide be \(h\). Using the Pythagorean theorem again \(h=\sqrt{c^{2}-b_{1}^{2}}\), where \(c\approx44.72\) and \(b_{1} = 35\).

$$h=\sqrt{(20\sqrt{5})^{2}-35^{2}}=\sqrt{2000 - 1225}=\sqrt{775}\approx27.8$$

Answer:

C. 27.8 ft