Question

How do you use special right triangles to solve for missing sides? (30-60-90 and 45-45-90 triangles)

Answer 1

Answer: see below

Explanation:

30 - 60 - 90 triangles have angles in the triangle measuring 30, 60, and 90 degrees. A 30 - 60 - 90 triangle also has special side ratios according to a side's location in the triangle.

The side across from the 30 degree angle is represented by x.

The side across from the 60 degree angle is represented by x
`√(3)`.

The side across from the 90 degree angle is represented by 2x.

45 - 45 - 90 triangles have angles in the triangle measuring 45, 45, and 90 degrees. A 45 - 45 - 90 triangle has special side ratios similar to the 30 - 60 - 90 triangle.

The side across from either of the 45 degree angles is represented by x.

The side across from the 90 degree angle is represented by x
`√(2)`.

These ratios can be used to find missing sides. If you know that a triangle is one of these special triangles and you also know one of its side lengths, you can plug the known length in for x in the proper place.

EX: you have a 30 - 60 - 90 triangle with a side length of 2 across from the 30 degree angle. You then know that the side across from 60 is 2
`√(3)` and the side across from 90 is 4.