Question

find the length of the unknown side of the right triangle. in each case, a and b represent the lengths of the legs and c represents the length of the hypotenuse. a=15, c=25, find b a. 20 b. 625 c. 850 d. 10

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are legs, \(c\) is hypotenuse. We need to solve for \(b\), so rearrange the formula: \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values of \(a\) and \(c\)

Given \(a = 15\), \(c=25\), substitute into the formula: \(b^{2}=25^{2}-15^{2}\). Calculate \(25^{2}=625\) and \(15^{2}=225\), so \(b^{2}=625 - 225=400\).

Step3: Solve for \(b\)

Take the square root of both sides: \(b=\sqrt{400}=20\) (since length can't be negative, we take the positive root).

Answer:

A. 20