A Leg That Is Not Whole

Part of the Triangles section of Coddy's Geometry journey. Lesson 28 of 60.

A leg can come out as a root too. Keep it exact and simplify, just as for a hypotenuse.

$Right triangle PQR with leg 4 and hypotenuse 6$

Here the hypotenuse is 6 and one leg is 4, so the other leg squared is $36-16 = 20$ . Since 20 = 4 × 5, the leg is $\sqrt{20} = 2\cdot \sqrt{5}$ . As a check, $2\cdot \sqrt{5}$ is about 4.5, shorter than the hypotenuse, as a leg must be.

Challenge

△ABC has a right angle at A. Find the exact length of 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

1The Triangle Inequality

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

4Area of a Triangle

Half the Rectangle Height Is Not a Side Right Triangle Area Finding the Height Any Side Can Be the Base Recap: Area

7Is It Right?

The Converse Testing a Triangle Acute or Obtuse?Sorting by the Test Recap: Right or Not

10Scale in the World

Shadows Across the River Nested Triangles A Side with an Expression Recap: Scale in the World

2Sides and Names

Sorting by Sides The Longest Side Ticks into Equations Recap: Sorting Triangles

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 Backwards The Ladder Which Side Is c?A Leg That Is Not WholeRecap: 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