Question

what are the exact side lengths of the triangle shown? 4 in. 45° c 45° b b = inches c = inches

Explanation:

Step1: Identify triangle type

This is a 45 - 45-90 right - triangle. In a 45 - 45-90 triangle, the legs are congruent. Given one leg is 4 inches, so $b = 4$ inches.

Step2: Use Pythagorean theorem for hypotenuse

For a right - triangle $a^{2}+b^{2}=c^{2}$. Since $a = 4$ and $b = 4$, then $c=\sqrt{4^{2}+4^{2}}=\sqrt{16 + 16}=\sqrt{32}=4\sqrt{2}$ inches.

Answer:

$b = 4$
$c = 4\sqrt{2}$