Question

What is the perimeter of a 30-60-90 triangle with a shortest side of 3

Will give brain

Answer 1

Answer: About 14.2 units.

Explanation:

It's given that this is a right triangle since there is a 90-degree angle.

Since this is a 30-60-90, a "special" triangle, it's given that the shortest side is opposite of the 30-degree angle. The hypotenuse is twice the shortest leg (3 units * 2 = 6 units). Lastly, the longer side is the square root of 3 times the shorter leg (
`√(3) *3=3√(3)`).

We can draw a diagram of this, see attached.

Lastly, we will solve for the perimeter by adding together all of the side lengths.

P = 3 units + 6 units +
`3√(3)` units = 3 + 6 + 5.1961524 ≈ 14.2 units