Question

Help! Find the missing side lengths. Leave the answers as radicals in simplest form.

Answer 1

Answer:

b = 3.5

a = 7

Step-by-step explanation:

Hello!

This triangle is a 30°-60°-90° triangle, as the missing angle is 30° and the other two angles are 60° and 90°.

There are some important Rules:

• The leg that is opposite to the 30° angle is half of the hypotenuse.
• The leg that is opposite to the 60° angle is the length of the leg opposite to the 30° multiplied by $\sqrt3$.

We can first solve for the leg that is opposite to the 30° angle.

Since $\frac{7\sqrt3}{2}$ is $b\sqrt3$:

• $\frac{7\sqrt3}{2} = b\sqrt3$
• $\frac72 = b$

The length of b is 3.5.

We can multiply 3.5 by 2 to find the length of a.

• $\frac a2 = b$
• $\frac a2 = \frac72$
• $a = 7$

The length of a is 7.