Q&A for How to Find the Length of the Hypotenuse

One common mistake is forgetting to square the terms. In the Pythagorean Theorem, all three terms are squared. Many people go too fast and forget to find the square before the sum of 'a' and 'b,' which gives them an incorrect answer.

Google provides a right angle triangle calculator that allows you to solve for the hypotenuse. Simply search for “hypotenuse calculator” and plug your numbers into the calculator at the top of the search results. You can also use the hypotenuse calculator at Omincalculator.com.

If you know you are dealing with a right triangle, then you already know that one of the angles is 90°. Since the angles must add up to 180°, you can solve for the missing angle using the formula 90 + X = 180. Once you have all 3 angles, you can use that information and the known length of 1 side to use the law of sines and find the length of the hypotenuse.

To get the area of a triangle, you need the base and the height or the length of all three sides. Since the angles are unknown, it is impossible.

Multiply the area by 2. Divide that by the known side. That gives you the other non-hypotenuse side. Find the square of each known side. Find the sum of those squares. Find the square root of that sum. That's the hypotenuse.

You would use the trigonometric functions (sine, cosine and tangent).

Yes. Use the Pythagorean theorem.

Yes, if you're prepared to apply trigonometry to the question.

Use the Pythagorean theorem to find the other side, which is also the height of the triangle. Half the base multiplied by the height is the area.

Yes. You would square the hypotenuse, then subtract from that the square of the base. That gives you the square of the "rise" (the other non-hypotenuse side). Find its square root, which gives you the rise (the other leg) of the right triangle.

You don't have enough information to find the two sides.

A scalene triangle is a triangle that has three unequal sides. You should be able to find the missing length if you know the other two sides. Use the Pythagorean Theorem ( a^2 + b^2 = c^2), using the two known lengths to represent a and b.

It depends on what your other sides are, what kind of triangle it is, and it also depends on whether you want the hypotenuse.

If you know the length of the base, you must also know the length of the other (non-hypotenuse) side in order to find the length of the hypotenuse. See Method 1 above.

You will also have to know the height before you can find the hypotenuse.

If it's an equilateral triangle, the two sides each have the same length as the base.

Assuming this is a right triangle, it's a matter of trigonometry. Use the sine, cosine, or tangent of any of the angles to calculate the unknown side.

Find the cosine of the angle by dividing the side by the hypotenuse, then look up the angle on a trig table.

You can't.

By doing a little algebra. Tan=o/a. So, find which one is unknown O or A. Then you will know both sides giving you enough info to apply the Pythagorean theorem.

Assuming you know only the area, then you can't. Imagine a triangle with a base one mile long and a side, let's say one millionth of an inch high, producing an area lets say one square inch. This would produce a hypotenuse. Slightly longer than a mile. Now visualize a smaller triangle that would fit on a sheet of paper that produces one square inch. The hypotenuse would be much shorter. Same square area but two very different hypotenuse s. You would need more info than just area.

Use the Pythagorean theorem: Square the hypotenuse. Subtract the square of the known leg. Find the square root of that difference. That's the leg you're looking for.

No. You would also have to know the other side or one of the acute angles.

That would be difficult if the triangle is large. Use Pythagorean's theorem to solve this.

Double the area. Then find the square root of that number. That equals the base (and the height) of the triangle. Square the base. Double that number. Then find this last number's square root. That's the hypotenuse. This works only for right isosceles triangles.

Given only that angle M equals 90°, all that we know is that angles B and L combine to make 90°. We cannot know what those angles are.

Yes. You would use trigonometry to find the other two sides.

49 + b² = 625. Subtract 49 from both sides of the equation. That means b² = 576, and b = 24.

a² + b² = c². 60² + 11² = 3600 + 121 = 3721 = c². So the hypotenuse (c) is √3721 = +/- 61. A hypotenuse cannot have a negative length, so it is 61 cm.

That's not enough information to calculate the hypotenuse. You need to know either both of the legs of the triangle or one side and at least one of the acute angles.