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?


145.6 ft

134.2 ft

9,000 ft

18,000 ft

Answer 1

To find the distance from the anchor to a point directly below the boat, we can use the Pythagorean theorem.

Let's denote:
- the length of the rope as \( r = 140 \) feet,
- the depth of the water (vertical distance from the boat to the ocean floor) as \( d = 40 \) feet,
- and the horizontal distance from the point directly below the boat to the anchor as \( h \).

According to the Pythagorean theorem:

\[
r^2 = d^2 + h^2
\]

Plugging in the values:

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

Calculating the squares:

\[
19600 = 1600 + h^2
\]

Now, subtract \( 1600 \) from both sides:

\[
19600 - 1600 = h^2
\]
\[
18000 = h^2
\]

Taking the square root of both sides to find \( h \):

\[
h = \sqrt{18000}
\]

Calculating \( \sqrt{18000} \):

\[
h \approx 134.164
\]

Rounding to the nearest tenth, we get:

\[
h \approx 134.2
\]

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