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# Need help solving 30 60 90 triangles for ACT prep

Hey guys, I'm preparing for the ACT. I keep encountering these 30 60 90 triangles in the ACT math section and I'm just not sure how to approach them. Can somebody break it down for me or share any tips or strategies?

27 days ago

Sure, I'd be happy to explain the 30 60 90 triangle for you!

A 30-60-90 triangle is a special kind of right triangle, where the three angles are 30 degrees, 60 degrees, and 90 degrees. The sides of a 30 60 90 triangle always follow a specific ratio, and that's what makes them so useful for problems in standardized tests like the ACT.

The ratio is as follows:

- The side across from the 30-degree angle equals to half the length of the hypotenuse.

- The side across from the 60-degree angle equals to the square root of three times the length of the side across from the 30-degree angle, or equivalently, it's the hypotenuse times root 3 divided by 2.

- The side across (opposite) the 90-degree angle is the longest side (the hypotenuse).

So, if you label the side across from the 30-degree angle as "x", then the side across from the 60-degree angle is "x√3", and the hypotenuse is "2x".

Here's a useful strategy: if you're given the length of one side, you can use the rules above to figure out the lengths of the other two sides. But pay close attention to which side length you're given. The ratio depends on which angle you're looking at.

Remembering the properties of the 30-60-90 triangle can save you significant time on these problems, so practice applying this knowledge with different problems and it should soon become second nature.

Let me know if you have any other questions!

27 days ago