Solving Special Right Triangles

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When solving special right triangles, remember that a 30-60-90 triangle has a hypotenuse twice as long as one of the sides, and a 45-45-90 triangle has two equal sides. Memorize rules that relate to special right triangles with instructions from a college-level math teacher in this free video on geometry.

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Video Transcript

So how does one solve those special right triangles? Hi, I'm Jimmy Chang; I've been teaching College Mathematics for nine years and yes, there are actually some very special right triangles out there. Right triangles that fit certain properties and along with some of those geometric postulates and theorems that you all know and love in the past; they come true in the special right triangles. We're going to explore two special right triangles today; 30-60-90 triangle and a 45-45-90 triangle. Now the first triangle, 30-60-90 is known because one angle is 30 degrees, another angle is 60 degrees and the third angle is 90 degrees. Now notice, the 60 degree angle is twice as much as the 30 degree angle. Now according to a 30-60-90 triangle, the side that's facing the 30 degree angle is going to be half as much the hypotenuse or put it in another way, the hypotenuse is going to be twice as long as the side facing the 30 degree angle. So for example, if the side facing the 30 degree angle is 2, then the hypotenuse in this 30-60-90 triangle is going to be twice as long; in other words, it's going to be 4 units. Also, the side that's facing the 60 degree angles is going to be square root of 3, that's right, square root of 3 times the side that's facing the 30 degree angle. So again, here's another example. If the 30 degree angle side is 2, then the side that's facing facing the 60 degree angle is going to be square root of 3 times that; in other words, 2 times square root of 3. That will always be the case. Now, here's what happens in a 45-45-90 triangle. Now in a 45-45-90 triangle, the two legs, the two sides that's supporting the right angle are equal. So that means, if this leg is 2, then this leg is also 2. Now, there is a property out there that says, in terms of the hypotenuse, the hypotenuse is going to be square root of 2 times the legs. In other words, if this side is 2, then just multiply square root of 2 and so you have the hypotenuse, having a length of 2 root of 2. But these are some of the properties of those special right triangles and I'm Jimmy Chang.

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