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Legs from the Hypotenuse

Part of the Triangles section of Coddy's Geometry journey. Lesson 39 of 63.

Going the other way, a leg is the hypotenuse divided by √2. Dividing by a root is awkward, so it is usually written with the root on top: multiply top and bottom by √2.

10/√(2) = (10×√(2))/2 = 5×√(2)

$Right triangle PQR with a 45 degree angle and hypotenuse 10$

So a 45-45-90 triangle with hypotenuse 10 has legs of 5×√(2). A quick way to see it: the leg is half the hypotenuse times √2. Check with Pythagoras: two legs squared are 50 + 50 = 100 = 10².

Challenge

△ABC has a right angle at B and a 45° angle at C. Its hypotenuse is 16. Find the leg BC, then press Check.

Try it yourself

$Find the marked part of the figure$

Find the marked part of the figure

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Triangles

2The Triangle Inequality

Can Three Sticks Meet?Exactly Reaching The Range of the Third Side The Formula Recap: The Third Side

5The Pythagorean Theorem

Squares on the Sides Finding the Hypotenuse Pythagorean Triples When It Is Not Whole Recap: The Hypotenuse

8Special Right Triangles

The 45-45-90 TriangleLegs from the HypotenuseThe 30-60-90 Triangle All Three Sides Which Triangle Is It?Recap: Special Triangles

11Two Tools at Once

Height of an Isosceles Area from the Height The Equilateral Triangle Right Triangle Perimeter Recap: Two Tools