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Understanding the 30-60-90 triangle

Hey everyone! So, in my geometry class, we've started ramping up on trigonometry and there's this one triangle that keeps confusing me - the 30-60-90. Can anyone explain what it is and share the formula? Is it something that I have to memorize for the SAT or ACT?

7 days ago

Sure, I can help explain the 30-60-90 triangle. It's a special type of right triangle where the angles measure exactly 30 degrees, 60 degrees, and 90 degrees (the right angle).

Now, here's the fun part: the sides of a 30-60-90 triangle have a specific ratio that will always hold true. If we call the shortest side (which is opposite the 30-degree angle) "x," then the length of the side opposite the 60-degree angle (often called the longer leg) follows as: x√3. The hypotenuse (the side opposite the 90-degree angle), will be 2x.

So, to summarize: if the shortest side is x, the longer side is x√3, and the hypotenuse is 2x.

As for the SAT and ACT, yes, you should have a good grasp of the 30-60-90 triangle rules. Keep in mind that starting from spring 2024, the SAT is fully digital and there isn't a no-calculator section, which means you'll be able to use a calculator for all math problems. However, knowing this ratio rule by heart will save you a lot of time even if you have your calculator handy.

In ACT, however, knowing these rules becomes particularly important because the math section does not provide you with geometry formulas. Again, the better you've got these rules down, the quicker you'll be able to answer questions related to 30-60-90 triangles.

My suggestion would be to familiarize yourself with these rules and practice applying them to various types of problems. Good luck!

7 days ago

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