A Leg That Is Not Whole

Part of the Triangles section of Coddy's Geometry journey. Lesson 38 of 71.

A leg can come out as a root, just as a hypotenuse can. With hypotenuse 7 and leg 2:

$A right triangle with hypotenuse 7, one leg 2 and the other leg a unknown$

Hypotenuse 7, leg 2

a = √(7^2 - 2^2) = √(45)

a = 3√(5)

45 has the square factor 9, so the root simplifies to 3√(5). 3√(5) is about 6.7, which is a little less than the hypotenuse 7, as a leg must be.

When the number under the root has no square factor, the root is the finished answer. Hypotenuse 6 and leg 1 give √(35). The rules for roots from the hypotenuse chapter are the same here. The only difference is that the squares are subtracted instead of added.