45-45-90 Triangles                    Page 3 of 5

The Shortcut for 45-45-90 Triangles

If you know the leg of a 45-45-90 triangle, you can find the hypotenuse by multiplying the leg by the square root of 2.

 
​Example 1
 Find b and c.

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​Answer:
The two legs of a 45-45-90 triangle are always the same length.  The legs are the two sides that form the right angle: the 5 and the b.  This means that b is also 5.  To find the hypotenuse, we can use the shortcut and simply multiply the leg by the square root of 2.

Example 2
 Find d and e.

Answer:
This one is slightly trickier because of the way the triangle has been drawn.  Remember,the legs of a right triangle form the right angle, the form the letter "L".  In this triangle, the two legs are d and 8: they form the 90 degree angle at the top.  The legs of a 45-45-90 triangle are always the same length so d = 8.  The hypotenuse is always across from the right angle. In this triangle, the hypotenuse is at the bottom of the triangle, the e.  To find the hypotenuse of a 45-45-90 triangle, you need to multiply the leg by the square root of 2.

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