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

for the right triangles below, find the exact values of the side lengths h and a. if necessary, write your responses in simplified radical form.

for the right triangles below, find the exact values of the side lengths h and a. if necessary, write your responses in simplified radical form.

Answer

Explanation:

Step1: Find h in the 45 - 45 - 90 triangle

In a 45 - 45 - 90 triangle, the legs are congruent. Given one leg is 2. So, $h = 2$.

Step2: Find a in the 30 - 60 - 90 triangle

In a 30 - 60 - 90 triangle, if the shorter leg (opposite 30°) is 4, and the side opposite 60° is related to the shorter leg by the ratio $\sqrt{3}$. So, $a = 4\sqrt{3}$.

Answer:

$h = 2$ $a = 4\sqrt{3}$