Here are a few triangle properties to be aware of: How do we know that the side lengths of the 30-60-90 triangle are always in the ratio \(1:\sqrt3:2\) ? While we can use a geometric proof, it’s probably more helpful to review triangle properties, since knowing these properties will help you with other geometry and trigonometry problems.
If you recognize the relationship between angles and sides, you won’t have to use triangle properties like the Pythagorean theorem. On standardized tests, this can save you time when solving problems. Knowing this ratio can easily help you identify missing information about a triangle without doing more involved math. Here is an example of a basic 30-60-90 triangle: The side opposite the 90 º angle has the longest length and is equal to \(2x\).The side opposite the 60º angle has a length equal to \(x\sqrt3\).The side opposite the 30º angle is the shortest and the length of it is usually labeled as \(x\).Because the angles are always in that ratio, the sides are also always in the same ratio to each other. Here’s what you need to know about 30-60-90 triangle.Ī 30-60-90 triangle is a right triangle with angle measures of 30 º, 60º, and 90º (the right angle).
Because its angles and side ratios are consistent, test makers love to incorporate this triangle into problems, especially on the no-calculator portion of the SAT. The 30-60-90 triangle is a special right triangle, and knowing it can save you a lot of time on standardized tests like the SAT and ACT.
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