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Keywords: Right triangle,isosceles right triangle,special right triangle
Common Core Standard G.SRT.6
A triangle with two equal sides, and a ninety degree angle will be a 45 45 90 triangle. Notice the triangle drawn inside a circle is a 45 45 90 because the radii are equal, and there is a 90 degree angle.
45-45-90 Triangle
45 45 90
45 45 90
As the name implies a 45-45-90 triangle has two angle measures of 45 degrees, and one of ninety degrees.
A forty five,forty five, ninety triangle has two equal sides.
The hypotenuse is always the longest side, and is opposite the right angle.
The length of the hypotenuse equals, leg length√2
The length of one leg of a 45-45-90 triangle equals, hypotenuse/√2
A helpful angle to side ratio to remember when working with 45 45 90 triangles is as follows:
45 45 90
x x x√2
The legs opposite the forty five degree angles are equal, and the hypotenuse which is opposite the 90 degree angle, is equal to x√2
You can also write this ratio as 1:1: √2
The formula for finding area equals ½(leg)2
A 45 45 90 triangle is also called an isosceles right triangle
The diagonal of a square creates two 45 45 90 triangles.
Questions answered in this video
If given the hypotenuse how do you find the leg length of a 45 45 90 triangle?
If given the leg length how do you find the hypotenuse of a 45 45 90 triangle?
What shortcuts can I use to find the leg lengths of a special right triangle easily?
Example 2. Find the length of the two sides of a 45-45-90 triangle with a hypotenuse length of 12 units.
Example 1: How to solve a 45 45 90 triangle. What is the length of the hypotenuse of a 45-45-90 triangle with a leg length of 7 units?
Related sites
Step 1. Use x√(2 ) x = leg length
Step 2. 7√(2 ) units
Identifying 45 45 90 triangles
Hypotenuse =
units
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Properties of a special right triangle 45 45 90
Shortcuts for finding 45 45 90 Triangle sides
We all love shortcuts. Try these for finding the side lengths of a 45 45 90 special right triangle.
Just remember √2
Hypotenuse = leg length x √2
Leg length = hypotenuse/√2
45 45 90 Triangles are special right triangles that have unique properties that allow one to find missing angles and side lengths.