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

Contents

## How do you determine the longest side of a triangle?

Concepts

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

## What is the longest side of the 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 side of a triangle given two sides?

Right Triangles and the Pythagorean Theorem

1. The Pythagorean Theorem, a2+b2=c2, a 2 + b 2 = c 2 , can be used to find the length of any side of a right triangle.
2. The side opposite the right angle is called the hypotenuse (side c in the figure).

## How do you find the side lengths of a triangle with all angles?

If you know two sides and the angle between them, use the cosine rule and plug in the values for the sides b, c, and the angle A. Next, solve for side a. Then use the angle value and the sine rule to solve for angle B. Finally, use your knowledge that the angles of all triangles add up to 180 degrees to find angle C.

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## What is the rule for finding the missing side of a triangle?

Finding the missing side of a right triangle is a pretty simple matter if two sides are known. One of the more famous mathematical formulas is a2+b2=c2 a 2 + b 2 = c 2 , which is known as the Pythagorean Theorem.

## 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 is the rule for side lengths 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.

## How do you find the third side of an obtuse triangle?

You can use the pythagorean theorem to see where the angle between the first two sides would be 90 degrees. Third side = sqrt(16^2 + 21^2) = 26.4.

## 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.

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