Question

william is deep - sea diving with two friends. lamar is exploring a coral reef 7 meters in front of william, and bruce is floating on the surface directly above william. if bruce and lamar are 10 meters apart, how far apart are william and bruce? if necessary, round to the nearest tenth.

Explanation:

Step1: Identify the right - triangle

The positions of William, Bruce, and Lamar form a right - triangle. The distance between Lamar and William is one leg ($a = 7$ meters), the distance between Bruce and Lamar is the hypotenuse ($c = 10$ meters), and the distance between Bruce and William is the other leg ($b$).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$. We want to find $b$, so we can rewrite the formula as $b=\sqrt{c^{2}-a^{2}}$.
Substitute $a = 7$ and $c = 10$ into the formula: $b=\sqrt{10^{2}-7^{2}}=\sqrt{100 - 49}=\sqrt{51}$.

Step3: Calculate the value

$\sqrt{51}\approx7.1$ (rounded to the nearest tenth).

Answer:

$7.1$