Question

For the right triangles below, find the exact values of the side lengths a and c. If necessary, write your responses in simplified radical form.

Answer 1

Answer:

First triangle: $a = 5\sqrt{2}$, second triangle: $c = \frac{8\sqrt{3}}{3}$

Step-by-step explanation:

In the first triangle, the value of $a$ is equal to the following trigonometric relation:

$a = \frac{5}{\cos 45^{\circ}}$

$a = \frac{5}{\frac{\sqrt{2}}{2} }$

$a = \frac{10}{\sqrt{2}}$

$a = \frac{10\sqrt{2}}{2}$

$a = 5\sqrt{2}$

In the second triangle, we obtain the value of $c$ is equal to the following trigonometric relation:

$c = 8\cdot \tan 30^{\circ}$

$c = 8 \cdot \left(\frac{\sin 30^{\circ}}{\cos 30^{\circ}} \right)$

$c = 8\cdot \left(\frac{\frac{1}{2} }{\frac{\sqrt{3}}{2} } \right)$

$c = \frac{8}{\sqrt{3}}$

$c = \frac{8\sqrt{3}}{3}$