# How do you use the 30 60 90 Triangle Theorem?

It turns out that in a 30-60-90 triangle, you can find the measure of any of the three sides, simply by knowing the measure of at least one side in the triangle. The hypotenuse is equal to twice the length of the shorter leg, which is the side across from the 30 degree angle.

Table of Contents

## Which triangle is a 30 60 90 triangle quizlet?

What is right triangle is a triangle with angle measures of 30°, 60°, and 90°. In a 30°-60°-90° right triangle, the measure of the hypotenuse is twice the measure of the short leg, and the measure of the longer leg is the measure of the short leg times √3 . You just studied 2 terms!

## What kind of triangle is 30-60-90?

In a 30°−60°−90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg. To see why this is so, note that by the Converse of the Pythagorean Theorem, these values make the triangle a right triangle.

## What type of triangle is a 45 45 90 right triangle?

A 45 45 90 triangle is a special type of isosceles right triangle where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees. Many times, we can use the Pythagorean theorem to find the missing legs or hypotenuse of 45 45 90 triangles.

## Are 30 60 90 triangles isosceles?

This is an isosceles right triangle. The other triangle is named a 30-60-90 triangle, where the angles in the triangle are 30 degrees, 60 degrees, and 90 degrees. Common examples for the lengths of the sides are shown for each below.

## How do you solve a 30 60 90 right triangle given only the hypotenuse?

In any 30-60-90 triangle, you see the following: The shortest leg is across from the 30-degree angle, the length of the hypotenuse is always double the length of the shortest leg, and you can find the length of the long leg by multiplying the short leg by the square root of 3.

## What is a 30 60 triangle?

A 30-60-90 triangle is a special right triangle (a right triangle being any triangle that contains a 90 degree angle) that always has degree angles of 30 degrees, 60 degrees, and 90 degrees. The side opposite the 60° angle will be the middle length, because 60 degrees is the mid-sized degree angle in this triangle.

## What kind of triangle is 60 60 60?

This is a 60-60-60 triangle (that is, an equilateral triangle), with all sides having a length of two units.

## How do you know if 3 sides make a right triangle?

Explanation: To check if the sides are a right triangle, check if the sum of the squares of the two smaller sides equals the length of the square of the longest side.

## Does 3/4 and 5 make a right triangle?

The 3:4:5 triangle is the best way I know to determine with absolutely certainty that an angle is 90 degrees. This rule says that if one side of a triangle measures 3 and the adjacent side measures 4, then the diagonal between those two points must measure 5 in order for it to be a right triangle.

## What are the 3 sides of a right triangle?

In a right triangle, the hypotenuse is the longest side, an “opposite” side is the one across from a given angle, and an “adjacent” side is next to a given angle. We use special words to describe the sides of right triangles.

## Why is the hypotenuse 1?

The hypotenuse is always the longest side of a right triangle, so these ratios will always be less than one.

## What is the perimeter of 30 60 90 triangle?

perimeter equals 30.05 in – adding all sides gives that result perimeter = a + a√3 + 2a = a(3 + √3) ≈ 30.05 in.

## Is triangle a degree?

A triangle’s angles add up to 180 degrees because one exterior angle is equal to the sum of the other two angles in the triangle. In other words, the other two angles in the triangle (the ones that add up to form the exterior angle) must combine with the third angle to make a 180 angle.

## Does 30 40 50 Make a right triangle?

Explanation: Pythagoras’s Theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides. Actually a 30 , 40 , 50 triangle is just a scaled up 3 , 4 , 5 triangle, which is a well known right angled triangle.

## Does 5 12 and 13 form a right triangle?

The first thing to recognize about this problem is that 5-12-13 is a Pythagorean triple. Any triangle composed of sides of lengths that match the Pythagorean triple will be a right triangle. That means our triangle has a 90 degree angle for angle C.

## How do you find a side length of a right triangle?

The converse of the Pythagorean Theorem is: If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

## Does 12 16 and 20 make a right triangle?

There is a fourth category of triangles in which one of interior angles is of 90∘ . It is called right triangle. It can be either be Scalene or Isosceles. 1) 12,16,20 : 202=162+122 : True, hence right triangle.

## Does 4 5 6 make right triangles?

Explanation: For a set of three numbers to be pythagorean, the square of the largest number should be equal to sum of the squares of other two. Hence 4 , 5 and 6 are not pythagorean triple.

## How do I find the third side of a triangle?

Pythagorean Theorem for the Third Side of a Right Angle Triangle. The Pythagorean Theorem is used for finding the length of the hypotenuse of a right triangle. So, as long as you are given two lengths, you can use algebra and square roots to find the length of the missing side.

## What do you mean by hypotenuse?

Definition of hypotenuse 1 : the side of a right-angled triangle that is opposite the right angle. 2 : the length of a hypotenuse.