# Shakuhachi.net

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# How do you find the length of the diagonal of a right-angled triangle?

## How do you find the length of the diagonal of a right-angled triangle?

To find the length of the diagonal (or hypotenuse) of a right triangle, substitute the lengths of the two perpendicular sides into the formula ​a2​ + ​b2​ = ​c2​, where ​a​ and ​b​ are the lengths of the perpendicular sides and ​c​ is the length of the hypotenuse.

### How do you find the hypotenuse of a right triangle using the Pythagorean theorem?

The hypotenuse formula is simply taking the Pythagorean theorem and solving for the hypotenuse, c . Solving for the hypotenuse, we simply take the square root of both sides of the equation a² + b² = c² and solve for c . When doing so, we get c = √(a² + b²) .

#### How do you find the length of a right angled triangle?

Key Takeaways

1. The Pythagorean Theorem, a2+b2=c2, a 2 + b 2 = c 2 , is used to find the length of any side of a right triangle.
2. In a right triangle, one of the angles has a value of 90 degrees.
3. The longest side of a right triangle is called the hypotenuse, and it is the side that is opposite the 90 degree angle.

How do I know if I have SOH CAH TOA?

The hypotenuse is always opposite the right angle. The sine of an angle is equal to the side opposite the angle divided by the hypotenuse….Sohcahtoa Calculator.

Soh… Sine = Opposite / Hypotenuse
…cah… Cosine = Adjacent / Hypotenuse
…toa Tangent = Opposite / Adjacent

Can you use SOH CAH TOA any triangle?

Q: Is sohcahtoa only for right triangles? A: Yes, it only applies to right triangles. A: They hypotenuse of a right triangle is always opposite the 90 degree angle, and is the longest side.

## How to find the hypotenuse of a triangle?

Find the longest side and label it the hypotenuse.

• The adjacent and opposite can only be found if you choose one of the non right angled angles.
• The adjacent is the side that forms the angle of choice along with the hypotenuse.
• The opposite is the side that does not form the angle of choice.
• 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.
• ### Does only a right triangle have a hypotenuse?

The hypotenuse side is opposite to the right angle, which is the biggest angle of all the three angles in a right triangle. Basically, the hypotenuse is the property of only the right triangle and no other triangle. Now, this is better explained when we learn about the right-angled theorem or Pythagoras Theorem or Pythagorean theorem.

#### Is the hypotenuse always the longest side of a triangle?

Thus, in a right triangle, the hypotenuse is always the longest side. The Pythagorean Theorem gives a beautiful relationship between the lengths of the sides in a right triangle: the sum of the squares of the shorter sides is equal to the square of the hypotenuse.

How do you find the hypotenuse?

You can find the length of the hypotenuse from two legs or a leg and an angle measure. The Pythagorean Theorem is a formula used to find the length of any of the sides of a right triangle when given two sides. The formula is usually expressed as a^2 + b^2 = c^2, where a and b are the legs, and c is the hypotenuse.