Question

Find a.

Write your answer in simplest radical form.

Answer 1

`a=10`

Explanation:

This problem can be solved in a ridiculous number of ways. However, it is likely introduced as a special-triangle problem in this question, because 4 pieces of information are given opposed to the necessary 3 to solve the triangle.

Special Right Triangles:

In any 30-60-90 triangle, all sides are in the proportion
`x:x√(3):2x`, where
`2x` is the hypotenuse and
`x` is the side opposite to the 30 degree angle. Since we notice that the side we're solving for is directly opposite to the 30 degree angle, we know that the side marked
`10√(3)` must be
`x√(3)` and therefore we have
`a=\boxed{10}`