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


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NOTES:

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?

142 + 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?

72 + k 2 = (16.55) 2  

49 + b 2 = 273.9

b2 = 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]

b2 = 4 [Subtracted 225 from both sides]

b = 2