3 Ways To Find The Length Of The Hypotenuse

Right angles are often notated in textbooks and on tests with a small square in the corner of the angle. This special mark means “90 degrees. "

If your triangle has sides of 3 and 4, and you have assigned letters to those sides such that a = 3 and b = 4, then you should write your equation out as: 32 + 42 = c2.

If a = 3, a2 = 3 x 3, or 9. If b = 4, then b2 = 4 x 4, or 16. When you plug those values into your equation, it should now look like this: 9 + 16 = c2.

In our example, 9 + 16 = 25, so you should write down 25 = c2.

In our example, c2 = 25. The square root of 25 is 5 (5 x 5 = 25, so Sqrt(25) = 5). That means c = 5, the length of our hypotenuse!

The first Pythagorean triple is 3-4-5 (32 + 42 = 52, 9 + 16 = 25). When you see a right triangle with legs of length 3 and 4, you can instantly be certain that the hypotenuse will be 5 without having to do any calculations. The ratio of a Pythagorean triple holds true even when the sides are multiplied by another number. For example a right triangle with legs of length 6 and 8 will have a hypotenuse of 10 (62 + 82 = 102, 36 + 64 = 100). The same holds true for 9-12-15, and even 1. 5-2-2. 5. Try the math and see for yourself! The second Pythagorean triple that commonly appears on tests is 5-12-13 (52 + 122 = 132, 25 + 144 = 169). Also be on the lookout for multiples like 10-24-26 and 2. 5-6-6. 5.

To calculate the hypotenuse of this triangle based on the length of one of the legs, simply multiply the leg length by Sqrt(2). Knowing this ratio comes in especially handy when your test or homework question gives you the side lengths in terms of variables instead of integers.

If you are given the length of the shortest leg (opposite the 30-degree angle,) simply multiply the leg length by 2 to find the length of the hypotenuse. For instance, if the length of the shortest leg is 4, you know that the hypotenuse length must be 8. If you are given the length of the longer leg (opposite the 60-degree angle,) multiply that length by 2/Sqrt(3) to find the length of the hypotenuse. For instance, if the length of the longer leg is 4, you know that the hypotenuse length must be 4. 62.

To find the sine of an 80 degree angle, you will either need to key in sin 80 followed by the equal sign or enter key, or 80 sin. (The answer is -0. 9939. ) You can also type in “sine calculator” into a web search, and find a number of easy-to-use calculators that will remove any guesswork. [10] X Research source

The Law of Sines can actually be used to solve any triangle, but only a right triangle will have a hypotenuse.

For example, if you know that A = 40 degrees, then B = 180 – (90 + 40). Simplify this to B = 180 – 130, and you can quickly determine that B = 50 degrees.

To continue our example, let’s say that the length of side a = 10. Angle C = 90 degrees, angle A = 40 degrees, and angle B = 50 degrees.

Using our example, we find that sin 40 = 0. 64278761. To find the value of c, we simply divide the length of a by this number, and learn that 10 / 0. 64278761 = 15. 6, the length of our hypotenuse!