# Is the hypotenuse always the shortest side?

## Is the hypotenuse always the shortest side?

The “c” is the hypotenuse, and although it represents the longest side of a right triangle, it is the shortest path between the two points on either end. But the hypotenuse isn’t always the shortest route. In fact, it is only the shortest one on football fields and other flat surfaces.

### Can the hypotenuse of a right triangle be shorter than the other two sides?

A hypotenuse does not have “sides” , so rephrase your question. Any side of a triangle is always shorter than the sum of lengths of the other two sides of the triangle. In a RIGHT TRINGLE, the SQUARE OF THE hypotenuse is ALWAYS EQUAL to the SUM OF THE SQUARES of the other two sides (called the LEGS) of the triangle.

Is the hypotenuse shorter than both sides?

Explanation: In any triangle sides, opposite to congruent angles, are congruent. A side, opposite to a bigger angle, is bigger than a side that lies opposite to a smaller angle. The largest angle in a right triangle is the right angle, therefore, opposite to it lies the longest side – hypotenuse.

What is the shortest side of a right triangle called?

hypotenuse
A right triangle has two shorter sides, or legs, and the longest side, opposite the right angle, which is always called the hypotenuse. The two shorter sides have some other special names, too, based on which acute angle of the triangle you happen to be working with at a particular time.

## Can the opposite side be bigger than the hypotenuse?

No, it can’t. The largest angle in a right triangle is 90 degrees and it is the largest angle of the triangle. The side opposite the largest angle has to be the largest side.

### Does the Pythagorean apply to all right triangles?

Pythagoras’ theorem only works for right-angled triangles, so you can use it to test whether a triangle has a right angle or not.

How do I know if I have SOH CAH TOA?

They are often shortened to sin, cos, and tan. The calculation is simply one side of a right-angled triangle divided by another side … we just have to know which sides, and that is where “sohcahtoa” helps….Sine, Cosine and Tangent.

Sine: soh sin(θ) = opposite / hypotenuse
Tangent: toa tan(θ) = opposite / adjacent

Is side A always longer than side B in a right triangle?

2 Answers. Side A and B does not matter when your trying to apply this to the pythagorean theorem but side C must always be the hypotenuse. The hypotenuse is always the triangle’s longest side. It is opposite the right angle.

## How do you find a 30 60 90 Triangle?

30-60-90 Triangle Ratio

1. Short side (opposite the 30 degree angle) = x.
2. Hypotenuse (opposite the 90 degree angle) = 2x.
3. Long side (opposite the 60 degree angle) = x√3.

### What is the Pythagorean theorem used for right triangles?

The Pythagorean theorem states that in any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the legs of the right triangle. This same relationship is often used in the construction industry and is referred to as the 3-4-5 Rule.

Which is the longest side of a right triangle?

The two legs meet at a 90° angle and the hypotenuse is the longest side of the right triangle and is the side opposite the right angle. The Pythagorean Theorem tells us that the relationship in every right triangle is:

Which is the smallest side of a right angle triangle?

The side opposite the right angle is the hypotenuese and is the longest. The side opposite the smaller of the two non-right angles will be the smallest side. The only exception I can think of is the special case of the 90-45-45 triangle.

## Is the hypotenuse always opposite the right angle?

The sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse . Usually, this theorem is expressed as A 2 + B 2 = C 2 . SOHCAHTOA only applies to right triangles ( more here) . The hypotenuse is the largest side in a right triangle and is always opposite the right angle.

### How is the hypotenuse of a right triangle solved?

The hypotenuse is opposite the right angle and can be solved by using the Pythagorean theorem. In a right triangle with cathetus a and b and with hypotenuse c, Pythagoras’ theorem states that: a² + b² = c². To solve for c, take the square root of both sides to get c = √(b²-a²).