Question

joey is deep - sea diving with two friends. isaac is exploring a coral reef 77 feet in front of joey, and adam is floating on the surface directly above joey. if adam and isaac are 85 feet apart, how far apart are joey and adam? feet

Explanation:

Step1: Identify the right triangle

We have a right triangle where the distance between Isaac and Joey is one leg (\(a = 77\) feet), the distance between Joey and Adam is the other leg (\(b\), which we need to find), and the distance between Adam and Isaac is the hypotenuse (\(c = 85\) feet). We use the Pythagorean theorem: \(a^{2}+b^{2}=c^{2}\).

Step2: Rearrange the formula to solve for \(b\)

We get \(b^{2}=c^{2}-a^{2}\). Substitute \(a = 77\) and \(c = 85\) into the formula: \(b^{2}=85^{2}-77^{2}\). Calculate \(85^{2}=7225\) and \(77^{2}=5929\). Then \(b^{2}=7225 - 5929=1296\).

Step3: Find the square root of \(b^{2}\)

Take the square root of both sides: \(b=\sqrt{1296}=36\).

Answer:

36