Question

5 multiple choice 1 point
note: figure not drawn to scale.
for the triangle shown, which expression represents the value of ( a )?
( sqrt{21^2 - 6^2} ) (triangle with hypotenuse 21, leg 6, leg ( a ), right angle)

Explanation:

Step1: Identify the triangle type

The triangle is a right - triangle (has a right - angle symbol). So we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with hypotenuse \(c\) and legs \(a\) and \(b\), \(c^{2}=a^{2}+b^{2}\).
In this triangle, the hypotenuse \(c = 21\), one leg \(b = 6\), and the other leg is \(a\).

Step2: Rearrange the Pythagorean theorem to solve for \(a\)

From \(c^{2}=a^{2}+b^{2}\), we can rearrange it to solve for \(a\). Subtract \(b^{2}\) from both sides of the equation: \(a^{2}=c^{2}-b^{2}\). Then take the square root of both sides: \(a=\sqrt{c^{2}-b^{2}}\).
Substitute \(c = 21\) and \(b = 6\) into the formula, we get \(a=\sqrt{21^{2}-6^{2}}\).

Answer:

\(\sqrt{21^{2}-6^{2}}\)