# How do you find the length of the longest triangle?

Contents

The longest side in a triangle is opposite the largest angle, and the shortest side is opposite the smallest angle. Triangle Inequality: In any triangle, the sum of the lengths of any two sides is greater than the length of the third side. Pythagorean Theorem: In a right triangle with hypotenuse c, a2+b2=c2.

## How do you find the missing length of a hypotenuse triangle?

1. If you are given the length of the shortest leg (opposite the 30-degree angle,) simply multiply the leg length by 2 to find the length of the hypotenuse. …
2. If you are given the length of the longer leg (opposite the 60-degree angle,) multiply that length by 2/Sqrt(3) to find the length of the hypotenuse.
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## How do you find the length of one side of a triangle?

If you have the hypotenuse, multiply it by sin(θ) to get the length of the side opposite to the angle. Alternatively, multiply the hypotenuse by cos(θ) to get the side adjacent to the angle. If you have the non-hypotenuse side adjacent to the angle, divide it by cos(θ) to get the length of the hypotenuse.

## How do you find the longest side of a right triangle?

The hypotenuse of a right triangle is always the side opposite the right angle. It is the longest side in a right triangle. The other two sides are called the opposite and adjacent sides.

## How do you find the length of the third side of a triangle?

If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

## How do you find the exact length of the third side?

The length of unknown third side of right triangle can be found by using Pythagoras theorem. a = √(c^2 – b^2) is the formula to find the length a:, b = √(c^2 – a^2) is the formula to find the length b: and c = √(a^2 + b^2) is the formula to find the length c:.

## Which is the length of the third side of the right triangle?

The side opposite the right angle is the hypotenuse. The Pythagorean theorem is used to solve for the length of the hypotenuse. If a right triangle has legs measuring a and b with hypotenuse c, the Pythagorean theorem is a² + b² = c².

## How do you find length?

To find Length or Breadth when Area of a Rectangle is given

1. When we need to find length of a rectangle we need to divide area by breadth.
2. Length of a rectangle = Area ÷ breadth.
3. ℓ = A ÷ b.
4. Similarly, when we need to find breadth of a rectangle we need to divide area by length.
5. Breadth of a rectangle = Area ÷ length.
6. b = A ÷ ℓ

## How do you find the side of a triangle given two sides and an angle?

“SAS” is when we know two sides and the angle between them. use The Law of Cosines to calculate the unknown side, then use The Law of Sines to find the smaller of the other two angles, and then use the three angles add to 180° to find the last angle.

## What is the shortest side of a right triangle?

In any triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle. Thus, in a right triangle, the hypotenuse is always the longest side.

## What are the 2 shorter sides of a right triangle called?

For a right triangle, the side that is opposite of the right angle is called the hypotenuse. This side will always be the longest side of the right triangle. The other two (shorter) sides are called legs.

## What are the side lengths of a 30 60 90?

A 30-60-90 triangle is a special right triangle whose angles are 30º, 60º, and 90º. The triangle is special because its side lengths are always in the ratio of 1: √3:2. Any triangle of the form 30-60-90 can be solved without applying long-step methods such as the Pythagorean Theorem and trigonometric functions.

## How do you find the third side of a triangle given two sides?

This means we are given two sides and one angle that is not the included angle. In this case, use The Law of Sines first to find either one of the other two angles, then use Angles of a Triangle to find the third angle, then The Law of Sines again to find the final side.

## What is the rule for the third side of a triangle?

Triangle Inequality Theorem. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

## Does 3 4 5 make right triangles?

This is one example of the many “pythagorean triples”. Any triangle whose sides are in the ratio 3:4:5 is a right triangle. … Such triangles that have their sides in the ratio of whole numbers are called Pythagorean Triples.