Download Article Show Download Article All right triangles have one right (90-degree) angle, and the hypotenuse is the side that is opposite or the right angle, or the longest side of the right triangle.[1] The hypotenuse is the longest side of the triangle, and it’s also very easy to find using a couple of different methods. This article will teach you how to find the length of the hypotenuse using the Pythagorean theorem when you know the length of the other two sides of the triangle. It will then teach you to recognize the hypotenuse of some special right triangles that often appear on tests. It will finally teach you to find the length of the hypotenuse using the Law of Sines when you only know the length of one side and the measure of one additional angle.
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About This ArticleArticle SummaryX If you need to find the length of the hypotenuse of a right triangle, you can use the Pythagorean theorem if you know the length of the other two sides. Square the length of the 2 sides, called a and b, then add them together. Take the square root of the result to get the hypotenuse. If you want to learn how to find the hypotenuse using trigonometric functions, keep reading the article! Did this summary help you? Thanks to all authors for creating a page that has been read 1,303,604 times. Did this article help you?How to find the side length of a right triangle?There are many ways to find the side length of a right triangle. We are going to focus on two specific cases. When we know 2 sides of the right triangle, use the Pythagorean theorem . We know 1 side and 1 angle of the right triangle, in which case, use sohcahtoa . If playback doesn't begin shortly, try restarting your device.
How do you find the angle of a right triangle?Their angles are also typically referred to using the capitalized letter corresponding to the side length: angle A for side a, angle B for side b, and angle C (for a right triangle this will be 90°) for side c, as shown below.
How do you work out the length of a triangle?You know the lengths of two sides of a triangle and the included angle. You can then work out the length of the remaining side using the cosine rule. You know all the lengths of the sides but none of the angles. Then, by rearranging the cosine rule equation: C = arccos ((a 2 + b 2 - c 2) / 2ab) The other angles can be worked out similarly.
How do you find the length of side adjacent to angle?sine (angle) = length of side opposite angle / length of hypotenuse. Therefore length of side opposite angle = length of hypotenuse x sine(angle) Similarly cos (angle) = length of side adjacent to angle / length of hypotenuse. Therefore length of side adjacent to angle = length of hypotenuse x cos(angle)
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