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

Explanation:

Step1: Find $h$ using tangent function

In the left - hand triangle with angle $60^{\circ}$, $\tan60^{\circ}=\frac{h}{4}$. Since $\tan60^{\circ}=\sqrt{3}$, we have $h = 4\tan60^{\circ}$. $h = 4\sqrt{3}$

Step2: Find $c$ using cosine function

In the right - hand triangle with angle $45^{\circ}$, $\cos45^{\circ}=\frac{c}{5}$. Since $\cos45^{\circ}=\frac{\sqrt{2}}{2}$, we can solve for $c$: $c = 5\cos45^{\circ}$. $c=\frac{5\sqrt{2}}{2}$

Answer:

$h = 4\sqrt{3}$ $c=\frac{5\sqrt{2}}{2}$