for the right triangles below, find the exact values of the side lengths d and c. if necessary, write your…

Explanation:

Step1: Find side length $d$ in the first right - triangle

In a 45 - 45 - 90 right - triangle, the legs are equal and if the hypotenuse is $h$ and the legs are $a$, then $h = a\sqrt{2}$. Given $h = 8$, and $h=\sqrt{2}d$. So, $d=\frac{8}{\sqrt{2}}$. Rationalize the denominator: $d=\frac{8\sqrt{2}}{2}=4\sqrt{2}$.

Step2: Find side length $c$ in the second right - triangle

In a 30 - 60 - 90 right - triangle, if the shorter leg (opposite the 30° angle) is $a$, the longer leg (opposite the 60° angle) is $a\sqrt{3}$, and the hypotenuse is $2a$. Given the shorter leg $a = 7$, and the hypotenuse $c$. Since the hypotenuse $c = 2a$, then $c = 2\times7=14$.

Answer:

$d = 4\sqrt{2}$ $c = 14$