# The hypotenuse of a right triangle

# The hypotenuse of a right triangle

In geometry, the hypotenuse is the side of a right triangle that is opposite to the right angle. The other two sides are called the legs of the triangle. The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

The term "hypotenuse" is derived from Greek, and it means "stretched under." In a right triangle, the hypotenuse is always the longest side. It is also sometimes referred to as the "major" or "longest" side. The two shorter sides are known as "legs," and they are usually labeled with letters corresponding to their respective angles: A for angle A, B for angle B, and so on.

To find the length of the hypotenuse, you can use either the Pythagorean theorem or trigonometry. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This formula is represented by:

### c^2 = a^2 + b^2

where c is the length of the hypotenuse, and a and b are lengths of the other two sides. This theorem is also sometimes called "Pythagoras's theorem."

You can also use trigonometry to find missing sides or angles in a right triangle. The most common trigonometric ratios are sine (sin), cosine (cos), and tangent (tan). These ratios are defined as follows:

sin(A) = opposite/hypotenuse

cos(A) = adjacent/hypotenuse

tan(A) = opposite/adjacent

Where A is an angle in a right triangle, and opposite and adjacent refer to sides that are opposite and adjacent to angle A, respectively.

## Conclusion:

In conclusion, in geometry, the hypotenuse is the side of a right triangle that is opposite to the rightangle .It maybefound usingthe Pythagoreantheorem . Trigonometrycan also be usedto find missing partsin a righttriangle .When tryingto findthe lengthofa line ,you must firstdetermineifthattriangleis arighttriangle .If so ,you c anusethe PythagoreanTheoremto solvefor c . However ,if you don'tknow ifthetriangleis arighttriangleor not ,you shoulddefaultto usingtrigonometryinstead.

## FAQ

### What is hypotenuse in simple words?

In simple terms, the hypotenuse is the longest side of a right angled triangle. It is the side opposite of the right angle and is usually denoted by the letter 'h'. To find the length of the hypotenuse, you can use either the Pythagorean theorem or trigonometry.

### Where is the hypotenuse?

The hypotenuse is always the side of a right triangle that is opposite to the right angle. In other words, it is the longest side of the triangle. It is also sometimes referred to as the "major" or "longest" side.

### How do you find the hypotenuse with Pythagorean theorem?

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This formula is represented by: c^2 = a^2 + b^2 where c is the length of the hypotenuse, and a and b are lengths of the other two sides.

### How do you find the hypotenuse example?

A common example of finding the length of the hypotenuse is using the Pythagorean theorem. In the formula, c^2=a^2+b^2, c is the hypotenuse and a and b are the other two sides. So, to find c, you would solve for c by taking the square root of a^2+b^2. For example, if a=3 and b=4, then c=5 because 3^2+4^2=25 and the square root of 25 is 5.

### What is the hypotenuse of a 1-1-sqrt 2 triangle?

The hypotenuse of a 1-1-sqrt 2 triangle is sqrt 2. This can be found by using the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the length of side a is 1, the length of side b is 1, and the length of side c is sqrt 2. Therefore, c^2=1^2+1^2=2 which means that the hypotenuse is sqrt 2.

### What is an example of a right triangle?

A common example of a right triangle is a 3-4-5 triangle. In this triangle, the length of side a is 3, the length of side b is 4, and the length of side c is 5. The hypotenuse is the longest side and is equal to 5. This can be verified by using the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, c^2=3^2+4^2=9+16=25 and the square root of 25 is 5.

### What are the different types of right triangles?

There are two different types of right triangles: the 3-4-5 triangle and the 30-60-90 triangle. The 3-4-5 triangle is a right triangle where the length of side a is 3, the length of side b is 4, and the length of side c is 5. The hypotenuse is the longest side and is equal to 5. The 30-60-90 triangle is a right triangle where the length of side a is 30, the length of side b is 60, and the length of side c is 90. The hypotenuse is the longest side and is equal to 90.

### What are the different parts of a right triangle?

The three parts of a right triangle are the hypotenuse, side a, and side b. The hypotenuse is the longest side and is opposite of the right angle. Side a and side b are the other two sides of the triangle that form the right angle.

### What is an obtuse triangle?

An obtuse triangle is a triangle where one of the angles is greater than 90 degrees. This means that the length of the hypotenuse will be greater than the length of either side a or side b.

### What is an acute triangle?

An acute triangle is a triangle where all of the angles are less than 90 degrees. This means that the length of the hypotenuse will be less than the length of either side a or side b.

### What is an equilateral triangle?

An equilateral triangle is a triangle where all of the sides are equal in length. This means that the lengths of side a, side b, and the hypotenuse will all be equal.

### What is an isosceles triangle?

An isosceles triangle is a triangle where two of the sides are equal in length. This means that either side a and side b will be equal, or side a and the hypotenuse will be equal, or side b and the hypotenuse will be equal.