Hey, pals. As if high school math wasn't enough, I'm prepping for the Math section of the ACT and stumbled upon this: ratio of sides for a 30-60-90 triangle. Anyone know what this ratio is and how can I remember it for the test?
Absolutely! The ratio of the sides of a 30-60-90 triangle is a pretty straightforward relationship that you'll often see on standardized tests like the ACT. In a 30-60-90 triangle, the lengths of the sides are as follows:
- The side opposite the 30° angle, also known as the shortest side, is often represented as x (or sometimes "a" in textbooks).
- The side opposite the 60° angle, which is the longer leg, is equal to x√3 (or "a√3").
- The side opposite the 90° angle, also known as the hypotenuse, is 2x (or 2a).
So, the ratio is 1:√3:2 (or sometimes written as x : x√3 : 2x).
To remember it, there's a little trick that I find useful. Think about the angles as time: "half past" (30 minutes past the hour, which represents our 30° angle), an "hour and a half" (or 90 minutes, standing for our 90° angle). Then picture what's left half way in between: "a full hour", which is 60 minutes for the 60° angle.
The "half past" is the shortest period of time, so it represents the shortest side x. The "hour and a half" is the longest time span, so it stands for the longest side 2x. And "full hour" or the 60 minutes that are in between, correspond to the intermediate side x√3. You might find this or other mnemonics online helpful for recalling this important rule!
CollegeVine’s Q&A seeks to offer informed perspectives on commonly asked admissions questions. Every answer is refined and validated by our team of admissions experts to ensure it resonates with trusted knowledge in the field.