30-60-90 triangle side lengths

Hey guys! I'm working on some trig stuff and I'm struggling with 30-60-90 triangles. Could someone explain how to find the side lengths of a 30-60-90 triangle? Thanks in advance!

Hey there! I'd be happy to help you with 30-60-90 triangles. A 30-60-90 triangle is a special right triangle, which means that its side lengths follow a specific ratio that's quite easy to remember. Here's the relationship between the side lengths in a 30-60-90 triangle:

1. The side opposite the 30-degree angle is the shortest side, and we can call it x.

2. The side opposite the 60-degree angle is the middle-length side, and it's equal to x √3.

3. The side opposite the 90-degree angle, the hypotenuse, is the longest side. It's double the shortest side, which means it's equal to 2x.

So, to summarize:

- 30-degree angle: x

- 60-degree angle: x √3

- 90-degree angle: 2x

When you're given a 30-60-90 triangle, typically you'll be provided one of the side lengths, and you can use the ratios mentioned above to find the other two side lengths. For example, if the shortest side (opposite to the 30-degree angle) is 5 units long, then the side opposite to the 60-degree angle is 5 √3 and the hypotenuse (opposite to the 90-degree angle) is 2 5 = 10 units long.

I hope this helps! Good luck with your trig work.