# How do you find the length of a leg of a 45 45 90 triangle with hypotenuse?

## How do you find the length of a leg of a 45 45 90 triangle with hypotenuse?

There is a ratio that all you need to do is take one of the legs and multiple by the square root of two to get the length of the hypotenuse. The two legs of a 45 45 90 are the same, and two times the square root two gives us the length of the hypotenuse.

How do you find the longer leg of a triangle?

You can multiply the short side by the square root of 3 to find the long leg. Type 2: You know the hypotenuse. Divide the hypotenuse by 2 to find the short side. Multiply this answer by the square root of 3 to find the long leg.

What is the length of the hypotenuse of a 45 45 90 triangle if the leg length is 6 centimeters?

8.5 cm
What is the length of the hypotenuse of a – – triangle if the leg length is 6 centimeters? SOLUTION: In a 45°-45°-90° triangle, the legs are congruent and the length of the hypotenuse h is times the length of a leg . ANSWER: or 8.5 cm eSolutions Manual – Powered by Cognero Page 6 8-3 Special Right Triangles Page 7 17.

### What is the longest side of a 45 45 90 Triangle?

hypotenuse
In a 45-45-90 triangle, the longest side has to be the hypotenuse. The other two sides would be the same (in this case, 5).

What is the 30 60 90 triangle rule?

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 are the rules for 45 45 90 triangles?

The main rule of 45-45-90 triangles is that it has one right angle and while the other two angles each measure 45° . The lengths of the sides adjacent to the right triangle, the shorter sides have an equal length.

#### What are the lengths of a 45 45 90 Triangle?

In its simplest form, the ratios of the length of sides in a 45 45 90 special right angle triangles should be 1 : 1 : 2 1:1:\sqrt{2} 1:1:2 . Recall that the 45 45 90 special right angle triangle is an isosceles triangles with two equal sides and the one larger side (i.e. hypotenuse definition).

How do you know if its at 45 45 90 triangle?

45 45 90 triangle rules and properties The most important rule is that this triangle has one right angle, and two other angles are equal to 45°. It implies that two sides – legs – are equal in length and the hypotenuse can be easily calculated. It’s the only possible right triangle that is also an isosceles triangle.

What are the lengths of a 45 45 90 triangle?

## How to find leg lengths of a 45 45 90 triangle?

How To Find Leg Lengths and Hypotenuse of a 45 45 90 Triangle 1 The angles, the two acute angles are two 45 degree angles, and are congruent. 2 Let’s look at the rules for 45- 45 -90. If you know one leg you know the other leg… 3 The two legs of a 45 45 90 are the same, and two times the square root two gives us the length…

How big is a 45° 45° 90° triangle?

Given that one angle of the right triangle is 45 degrees, this must be a 45°-45°-90° right triangle. Therefore, we use the n: n: n√2 ratios. Hence, the length of each side of the triangle is 3 inches.

What is the length of the legs opposite the 45° angle?

The legs opposite the 45° angles (the shorter sides) are of the length of the hypotenuse (the side opposite the 90° angle) The hypotenuse is times the length of either leg.

### Is the 45 45 90 triangle an isosceles triangle?

The other interesting properties of the 45 45 90 triangles are: It’s the only possible right triangle that is also an isosceles triangle. It has the smallest ratio of the hypotenuse to the sum of the legs.