How do I find the sides of a 30-60-90 triangle?

Hey y'all, I'm trying to figure out how to find the sides of a 30-60-90 triangle. I already know the angles, but I'm struggling with finding the side lengths. What's the formula I should use, and how does it work?

Hey there! To find the sides of a 30-60-90 triangle, you can use the following relationships between the sides:

1. The side opposite the 30-degree angle (let's call it side a) is half the length of the hypotenuse (let's call it side c). In other words, a = (1/2)c.

2. The side opposite the 60-degree angle (let's call it side b) is equal to the square root of 3 times the side opposite the 30-degree angle (side a). So, b = a √3.

If you're given the length of one side, you can use these relationships to find the other two sides. Here's an example:

Let's say you have a 30-60-90 triangle where the hypotenuse (side c) is 10 units long. To find the other sides, apply the relationships above:

1. a = (1/2)c = (1/2)10 = 5 units

2. b = a √3 = 5 √3 ≈ 8.66 units

Now you know the side lengths of the 30-60-90 triangle: side a is 5 units, side b is approximately 8.66 units, and side c is 10 units.