Question

examine this right triangle. which equation can be used to find the missing leg in the triangle?
$a^{2}+20^{2}=16^{2}$
$20^{2}+16^{2}=a^{2}$
$a^{2}+16^{2}=20^{2}$
$16+a^{2}=20$

Explanation:

Step1: Recall the Pythagorean theorem

For a right - triangle, the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (the longest side) and \(a\) and \(b\) are the legs.

Step2: Identify the sides

In the given right - triangle, one leg \(b = 16\) m, the hypotenuse \(c=20\) m, and the other leg is \(a\).

Step3: Substitute into the Pythagorean theorem

Substituting \(b = 16\) and \(c = 20\) into \(a^{2}+b^{2}=c^{2}\), we get \(a^{2}+16^{2}=20^{2}\)

Answer:

\(a^{2}+16^{2}=20^{2}\)