Question

A scuba diver has a taut rope connecting the dive boat to an anchor on the ocean floor. The rope is 140 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?

1) 134.2 ft
2) 18,000 ft
3) 9,000 ft

Answer 1

Using the Pythagorean theorem, the anchor is approximately 134.2 feet from a point directly below the boat when the rope is 140 feet long and the depth of water is 40 feet.

Step-by-step explanation:

To calculate how far the anchor is from a point directly below the boat, we use the Pythagorean theorem because we have a right triangle where the rope is the hypotenuse, the depth of the water is one leg, and the distance from the anchor to the point below the boat is the other leg.

Let x be the distance from the anchor to the point directly below the boat. According to the Pythagorean theorem:

Depth2 + x2 = Rope length2

Substitute the known values:

402 + x2 = 1402

1600 + x2 = 19600

x2 = 19600 - 1600

x2 = 18000

x = √18000

x ≈ 134.2 feet (to the nearest tenth of a foot)

Therefore, the anchor is approximately 134.2 feet from a point directly below the boat to the nearest tenth of a foot.