Question

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

Answer 1

b = 3.5

a = 7

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
`(7\sqrt3)/(2)` is
`b\sqrt3`:

• 
  `(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.