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Working Backwards

Part of the Triangles section of Coddy's Geometry journey. Lesson 28 of 63.

The theorem also finds a leg when you know the hypotenuse and the other leg. The hypotenuse square is the biggest, so take the known leg's square away from it.

$Right triangle PQR with leg 5 and hypotenuse 13$

Here 5^2 + b^2 = 13^2, so b^2 = 169 - 25 = 144, and the leg is 12. The usual slip is to add the squares, which would give a leg longer than the hypotenuse. A leg is always shorter than the hypotenuse, so check that.

Challenge

△ABC has a right angle at A. Find the leg AB, 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 Triangle Legs from the Hypotenuse The 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

3Perimeter

Around the Edge A Missing Side Isosceles Perimeter Sides as Expressions Recap: Around the Edge

6Finding a Leg

Working BackwardsThe Ladder Which Side Is c?A Leg That Is Not Whole Recap: Finding a Leg

9Similar Triangles

Same Shape, Different Size The Scale Factor Finding a Side Matching the Corners Recap: Similar Triangles

12Final Challenges

Final: Three Sticks Final: The Fence Final: The Ladder Final: The Shadow Final: Master of Triangles