Hello all, I'm studying trig right now and I'm stumped by this 30 60 90 ratio concept. I get that it's about triangles but how does it exactly work? And how significant is it on the SATs or ACTs? Any explanations would be helpful. Cheers!
Hello! I'm glad that you're taking the initiative to understand concepts that confuse you. The 30-60-90 triangle is a special kind of right triangle, so named because its three angles measure 30 degrees, 60 degrees, and 90 degrees.
So how does it work? When you have a 30-60-90 triangle, the ratios of the lengths of its sides are always constant: the side opposite the 30-degree angle is 1 unit long (this side is referred to as the "short leg"), the side opposite the 60-degree angle is sqrt(3) units long (this side is referred to as the "long leg"), and the side opposite the 90-degree angle - which is the hypotenuse, is always 2 units long. So if you know one of the side lengths, you can easily figure out the other two by multiplying or dividing by these values.
To give you an example, if the length of the side opposite the 30-degree angle (the short leg) is 5, then the hypotenuse is twice that, or 10, and the long leg is 5 sqrt(3).
Now, when it comes to the SAT and ACT, both tests cover geometry problems, and it's highly likely that you'll see at least a question or two that involve understanding of the 30-60-90 triangle. Being familiar with this concept could be a big time saver for you on the test, because you can quickly solve certain problems without needing to work out all the steps of the Pythagorean theorem.
Remember though, the SAT and ACT are about your overall understanding of a range of topics, so while it's good to master this concept, you will also need to be comfortable with other areas. Keep working at it!
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