Question

stacy is deep - sea diving with two friends. maggie is exploring a coral reef 21 meters in front of stacy, and terrence is floating on the surface directly above stacy. if terrence and maggie are 29 meters apart, how far apart are stacy and terrence? meters

Explanation:

Step1: Recognize the right - triangle

Stacy, Maggie, and Terrence form a right - triangle. Let the distance between Stacy and Terrence be \(x\) meters. Maggie is 21 meters from Stacy (one leg of the right - triangle), and Terrence and Maggie are 29 meters apart (the hypotenuse of the right - triangle).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a,b\) are the legs. Here, \(a = 21\), \(c = 29\), and \(b=x\). So, \(x^{2}+21^{2}=29^{2}\).
First, calculate \(21^{2}=441\) and \(29^{2}=841\). Then the equation becomes \(x^{2}+441 = 841\).
Subtract 441 from both sides: \(x^{2}=841 - 441\).
\(x^{2}=400\).
Take the square root of both sides: \(x=\sqrt{400}\).

Answer:

20