What is the length of a leg of a right triangle if the hypotenuse is 13 and the other leg is 5?

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To use the right angle calculator simply enter the lengths of any two sides of a right triangle into the top boxes. The calculator will then determine the length of the remaining side, the area and perimeter of the triangle, and all the angles of the triangle.

How to Find the Area and Sides of a Right Triangle

Do it yourself

If we know just two sides of a right triangle, we can use that information to find the third side, the area and perimeter of the triangle, and all the angles of the triangle. Amazing, right? Let’s review how we would find each of those parts.

How to find the Missing Side of a Right Triangle

To find the missing side of a right triangle we use the famous Pythagorean Theorem.

We need to be a little careful that we know which side we’re finding. Right triangles have two legs and a hypotenuse, which is the longest side and is always across from the right angle. When we’re trying to find the hypotenuse we substitute our two known sides for a and b. It doesn’t matter which leg is a and which is b. Then we solve for c by adding the squared values of a and b and taking the square root of both sides. 

When we’re trying to find one of the legs we enter the known leg for a and the known hypotenuse for c. Then we solve for b using simple algebra (subtract the value of a squared from both sides, then take the square root of both sides). 

How to find the Area of a Right Triangle

To find the area of a right triangle we only need to know the length of the two legs. We don’t need the hypotenuse at all. That’s because the legs determine the base and the height of the triangle in every right triangle. So we use the general triangle area formula (A = base • height/2) and substitute a and b for base and height. So our new formula for right triangle area is A = ab/2. 

How to find the Perimeter of a Right Triangle

To find the perimeter, or distance around, our triangle we simply need to add all three sides together. If we only know two of the sides we need to use the Pythagorean Theorem first to find the third side. 

How to find the Angles of a Right Triangle

To find the angles of a right triangle we use trigonometry. It’s not as difficult as it sounds. We just need to find one special button on our handheld calculators. To start we’ll need to know all the side lengths, so if we don’t know them already we’ll use the Pythagorean Theorem to find them first. 

Once we have all the sides we determine which angle we’re going to find. Then we take the side opposite that angle and divide it by the length of the hypotenuse, which is side c. That will give us a value between 0 and 1. Now we just need to find the ARCSIN button on our calculator, which is often labeled as SIN-1.  Finding the ARCSIN of our decimal value gives us our angle. Be sure that the calculator is set for angle mode rather than radian mode. 

We can repeat this process to find the other unknown angle in the triangle by once again dividing its opposite side by the hypotenuse and then taking the ARCSIN. 

Or we could show off even more triangle knowledge by using subtraction to find it since we know the interior angles of a triangle have to add up to 180°. Subtracting the angle we just found from 180° and then subtracting our known right angle (90°) will give us the third angle too. 

This calculator is great for getting all this information from just two sides of a right triangle, but it’s a fun challenge to try to find the sides, angles, area and perimeter on our own without it. Then you can use it to check our answers.

With this hypotenuse calculator you will quickly find this longest side of a right triangle. If you want to know what is the hypotenuse of a right triangle, how to find it and what is the hypotenuse of a triangle formula, you'll find the answer below, with a simple example to clear things up. Don't wait any longer, give this hypotenuse calculator a try!

A hypotenuse is the longest side of a right triangle. It's the side that is opposite to the right angle (90°). Hypotenuse length may be found, for example, from the Pythagorean theorem.

This hypotenuse calculator has a few formulas implemented - this way, we made sure it fits different scenarios you may encounter. You can find the hypotenuse:

1. Given two right triangle legs

Use the Pythagorean theorem to calculate the hypotenuse from right triangle sides. Take a square root of sum of squares:

• c = a / sin(α) = b / sin(β), from the law of sines

As area of a right triangle is equal to a * b / 2, then

• c = √(a² + b²) = √(a² + (area * 2 / a)²) = √((area * 2 / b)² + b²)

Let's calculate how long the ladder should be if we want to rescue a kitten from a 10 ft roof. The calculator helps to find the ladder length from the ground to the edge of the roof, but don't forget about a ladder part which should extend over the edge!

1. Choose the option needed for your calculations. We know that our roof is 10 ft in height and that the safest angle for a ladder is ~75.5°. From the dropdown list of the given box, select the option: angle ∡ and one side.
2. Change the units to feet.

1. Enter the given values. Our leg a is 10 ft long, and the α angle between ladder and ground equals 75.5°.

2. Ladder length, which is our right triangle hypotenuse, appears! It's equal to 10.33 ft.

   The angle β = 14.5° and leg b = 2.586 ft are displayed as well. The second leg is also an important parameter, as it tells you how far the ladder should be removed from the wall (or rather from a roof edge). The general principle to remember is a 4:1 rule – for every four feet of vertical height, the ladder foot should move one foot from the wall.

1. Perform the sin operation on the angle (not the right angle).
2. Divide the length of the side opposite the angle from step 1 by the result of step 1.
3. The result is the hypotenuse.

Yes, the hypotenuse is always the longest side, but only for right angled triangles. For isosceles triangles, the two equal sides are known as the legs, while in an equilateral triangle all sides are known simply as sides.

1. Find the longest side and label it the hypotenuse.
2. The adjacent and opposite can only be found if you choose one of the non right angled angles.
3. The adjacent is the side that forms the angle of choice along with the hypotenuse.
4. The opposite is the side that does not form the angle of choice.

1. Draw the altitude of the hypotenuse on the triangle. The two new triangles you have created are similar to each other and the main triangle.
2. Divide the length of the shortest side of the main triangle by the hypotenuse of the main triangle.
3. Multiply the result by the length of the remaining side to get the length of the altitude.
4. Alternatively, the angles within the smaller triangles will be the same as the angles of the main one, so you can perform trigonometry to find it another way.

If the hypotenuse is the opposite, then you are considering the wrong angle - you cannot use trigonometry with right angle of a triangle. Consider one of the other angles, and the opposite will be the side that does not form that angle.

1. Acquire a pair of compasses, a ruler, and a pen or pencil.
2. Set your pair of compasses to the length of the hypotenuse (or any length, as long as it stays constant).
3. Draw a circle that has its center at one of the ends of the hypotenuse.
4. Draw another circle with its center at the other end of the hypotenuse.
5. Draw a line joining the two points where these circles meet. This line is the hypotenuse.

1. Find the length of one of the non-hypotenuse sides.
2. Square the length of the side.
3. Double the result of the previous step.
4. Square root the result of step 3. This is the length of the hypotenuse.

The hypotenuse angle theorem is a way of testing if two right angled triangles are congruent or not. It states that if two right angled triangles have a hypotenuse and an acute angle that are the same, they are congruent.

The word hypotenuse comes from the Ancient Greek hypoteinousa, meaning ‘stretching under (a right angle)’. This, in turn, comes from hypo- ‘under’, and teinein ‘to stretch’. Another thing we have to thank the Ancient Greeks for!

You cannot solve a right angled triangle with only the hypotenuse. This is because the other two sides and angles are still undefined and therefore the triangle can still have many forms.