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 - angled triangle

Let the distance between William and Lamar be one leg ($a = 7$ meters), the distance between William and Bruce be the other leg (let it be $b$), and the distance between Bruce and Lamar be the hypotenuse ($c = 10$ meters).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. 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 of $b$

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

Answer:

$7.1$