Give these a try  1. X 2 = 49  2. X 2 = 48  3. X 2 + 144 = 169  4. X 2 + 3 2 = 5 2  1. 7 or –7  2. 6.93 or –6.93  3. 5 or –5  4. 4 or -4.

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Presentation transcript:

Give these a try  1. X 2 = 49  2. X 2 = 48  3. X = 169  4. X = 5 2  1. 7 or –7  or –6.93  3. 5 or –5  4. 4 or -4

Pythagorean Theorem

Essential Question  How do I use the Pythagorean Theorem to solve problems?

Vocabulary Hypotenuse: side opposite the right (90°) angle in a right triangle Longest side in a right triangle Legs (of a right triangle): two sides that form the right angle in the right triangle Pythagorean Theorem: a 2 + b 2 = c 2 a b c

Ex.1) Find the missing side length. Use the Pythagorean Theorem to find the length of a missing side of a right triangle. c 2 = c 2 = 233 c =  233  15.26

Ex. 2) Find the length of the missing side.  Do you know a? b? c?  a, b, and c are just variables.  In this example, x is the hypotenuse!  = x 2  = x 2  149 = x 2 X 10 7

What if a leg is missing?  Legs are 12, Y  Hypotenuse is 25  y 2 = 25 2  y 2 = 625  Y 2 = Y *** Why is –21.93 NOT an option? You can’t have a (-) length.

You Try!  Find the missing length of the two triangles.  = x 2  = z 2  x = X 2 2 z

 Decide whether the set of numbers can represent the side lengths of a right triangle.  5, 11, 16  ?= 16 2  ?= 256  146 = 256

 Are these sides for a Right Triangle???  NO!!! Which # is the hypotenuse!!!

Real-life!!  Your boat is traveling due north at 20 miles per hour.  A friend’s boat left at the same time from the same location headed due west at 15 miles per hour.  After an hour, your friend calls. He has engine trouble!!  How far are you going to have to travel to get to him????

Continued: Draw a picture. It Helps  Think….  = ? 2  25  You would have to travel 25 miles to get to your friend!!! 15 mi 20 mi

Think about it  What are the parts of a Rt. Triangle?  What is the Pythagorean Theorem?  Hypotenuse, 2 legs  leg 2 + leg 2 = hyp 2