Question

select the correct answer.
a boat is anchored in the water. the anchor lies at point a. at low tide, the boat is floating 20 feet above the seabed 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.

approximately how high is the boat floating above the seabed at high tide? assume the anchor rope remains tight, without any slack.
a. 27.8 ft
b. 15.6 ft
c. 35.7 ft
d. 32.5 ft

Explanation:

Step1: Calculate the length of the anchor rope

Use the Pythagorean theorem \(c = \sqrt{a^{2}+b^{2}}\) for the low - tide triangle. Here \(a = 20\) and \(b = 40\).

$$c=\sqrt{20^{2}+40^{2}}=\sqrt{400 + 1600}=\sqrt{2000}=10\sqrt{20}\approx44.72$$

Step2: Calculate the height at high tide

Let the height at high tide be \(h\). Using the Pythagorean theorem again \(c^{2}=h^{2}+35^{2}\). Since \(c\approx44.72\), we have \(h=\sqrt{c^{2}-35^{2}}\)

$$h=\sqrt{2000 - 1225}=\sqrt{775}\approx27.8$$

Answer:

A. \(27.8\) ft