What is so special about a 45-45-90 Triangle?

A 45-45-90 triangle is classified as a special right triangle, but why is it special? Let’s look at the special rules of a 45-45-90 Triangle.

Rule 1. If you know the length of one leg you know the length of the other leg because they are equal.

Rule 2. In order to find the length of the hypotenuse multiply the leg length times the square root of two. This would be written x√2 where x=leg length

Rule 3. In order to find the leg length divide your hypotenuse by the square root of 2. This may be written x/√(2 ) x=hypotenuse

Rule 4 .The area of a 45-45-90 triangle equals 1/2(leg)^2

Let’s look at two examples.

Example 1 Find the hypotenuse of a 45-45-90 triangle with leg length of 7 units.

Step 1. Use x√(2 )

Step 2. 7√(2 ) units

Example2. What is the length of one leg of a 45-45-90 triangle if you have a hypotenuse with a length of 12 units?

Step 1. 12/√2 use the formula for leg length hypotenuse divided by square root two

Step 2. 12/√2* √2/√2

Step 3. (12√2)/2 =6√2 units is the length of a leg