Question

How do I solve this???

Answer 1

To solve this answer, you must understand the side ratios that come with special right triangles.

There are 2 special right triangles, both identified by their angles.

• 45-45-90 triangles
• 30-60-90 triangles

Both triangles come with side ratios.

30-60-90 triangles have side ratios of x:x
`√(3)`:2x

45-45-90 triangles have side ratios of x:x:x
`√(2)`

The triangle in this question is a 45-45-90 triangle meaning the side ratios follow the x:x:x
`√(2)` format.

You have been given the side length of 6

As the side with the length of 6 is across the angle 45°, then this angle is one of the x's in the ratio x:x:x
`√(2)`

The next 45° angle is facing y, meaning that side also has the length of 6.

To find x, you can just plug in x into x
`√(2)`, leaving you with the side length

6
`√(2)`

Your angle lengths are 6,6 and 6
`√(2)`