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?

Question

145.6 ft

134.2 ft

9,000 ft

18,000 ft

Answer 1

To determine how far the anchor is from the point directly below the boat, we can use the Pythagorean theorem.

1. The length of the rope (hypotenuse) is 140 feet.
2. The depth of the water (one leg of the right triangle) is 40 feet.
3. The distance from the point directly below the boat to the anchor on the ocean floor will be the other leg of the triangle.

Let \( x \) be the horizontal distance from the point directly below the boat to the anchor. According to the Pythagorean theorem, we have:

\[ x^2 + 40^2 = 140^2 \]

Calculating \( 40^2 \) and \( 140^2 \):

\[ 40^2 = 1600 \] \[ 140^2 = 19600 \]

Now, substituting these values back into our equation:

\[ x^2 + 1600 = 19600 \] \[ x^2 = 19600 - 1600 \] \[ x^2 = 18000 \]

Taking the square root of both sides gives:

\[ x = \sqrt{18000} \] \[ x = 134.164 \text{ feet} \approx 134.2 \text{ feet} \]

Thus, the distance from the point directly below the boat to the anchor is approximately 134.2 feet.

The correct answer is: 134.2 ft.