60 30 90 Triangle Rules?

Yo, I'm studying for a geometry test and I just can't seem to wrap my head around the 60 30 90 triangle rules. Could anyone break it down for me, and maybe provide a few examples? Just trying to prepare for the SAT Math section too. Thanks in advance!

Hey! Sure, let's break down the 60-30-90 triangle rules for you. A 60-30-90 triangle is a specific type of right triangle that has angles of 60, 30, and 90 degrees. The sides of a 60-30-90 triangle follow a specific ratio, making it easier to find their lengths given just one side.

The rules are as follows:

1. The side that is opposite the 30° angle (the shortest side) is half the length of the side that is opposite the 90° angle (the hypotenuse).

2. The side that is opposite the 60° angle (middle-length side) is √3 times the length of the side that is opposite the 30° angle.

To make it simpler, consider the sides of the triangle to be as follows:

- Shortest side (opposite 30° angle): x

- Middle-length side (opposite 60° angle): x√3

- Hypotenuse (opposite 90° angle): 2x

Here are a few examples:

Example 1:

Given the shortest side (30°) with length 4, find the other two sides:

Shortest side (x) = 4

Middle-length side (x√3) = 4√3

Hypotenuse (2x) = 2×4 = 8

So, the triangle sides are 4, 4√3, and 8.

Example 2:

Given the hypotenuse (90°) with length 10, find the other two sides:

Hypotenuse (2x) = 10

Shortest side (x) = 10/2 = 5

Middle-length side (x√3) = 5√3

So, the triangle sides are 5, 5√3, and 10.

Knowing these 60-30-90 triangle rules will definitely come in handy for your geometry test and the SAT Math section. Good luck!