Pythagorean 1 Practice Sign In (NEW, See examples at bottom!!)

Pythagorean Theorem: a ^{2} + b ^{2} = c ^{2 }Where a and b are the lengths of the legs of a RIGHT triangle and c is the length of the hypotenuse. If you have two of these measures, you can find the length of the remaining one.

Example 1

A right triangle has legs z and y. One measures 14 and the other measures 16. How long is hypotenuse x?

14^{2} + 16 ^{2} = x ^{2}

196 + 256 = x ^{2}

452 = x ^{2}

21.3 = x (Taking the square root and rounding to the nearest tenth)

Example 2

A right triangle has a leg j that measures 7. The hypotenuse i measures 16.55. How long is the other leg k?

7^{2} + k ^{2} = (16.55) ^{2}

49 + b ^{2} = 273.9 ^{}

b^{2} = 224.9 [Subtracted 49 from both sides]

b = 15.0 [Rounded]

Example 3

A right triangle has ASM has a right angle at A. Side MS measures the square root of 229 and side AM measures 15. How long is SA?

(NOTE: MS is the hypotenuse!!)

15 ^{2} + b ^{2} = (root 229) ^{2}

225 + b ^{2} = 229 [NOTE: Square root of anything squared is itself] ^{}

b^{2} = 4 [Subtracted 225 from both sides]

b = 2