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Pythagorean Theorem What is it??

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Presentation on theme: "Pythagorean Theorem What is it??"— Presentation transcript:

1 Pythagorean Theorem What is it??
The Pythagorean Theorem describes the relationship between the side lengths in a right angle triangle.

2 What is a right triangle?
hypotenuse leg right angle leg It is a triangle which has an angle that is 90 degrees. The two sides that make up the right angle are called legs. The side opposite the right angle is the hypotenuse.

3 The Pythagorean Theorem
In a right triangle, if a and b are the measures of the legs and c is the hypotenuse, then a2 + b2 = c2. Note: The hypotenuse, c, is always the longest side.

4 1. Find the length of the hypotenuse if a = 12 and b = 16.
c a a2 + b2 = c2 (12)2 + (16)2 = c2 = c2 400 = c2 Take the square root of both sides. 20 = c b

5 2. Find the length of the hypotenuse if a = 5 and b = 7.
a2 + b2 = c2 (5)2 + (7)2 = c2 = c2 74 = c2 Take the square root of both sides. 8.6 = c c a b

6 Find the length of the leg, to the nearest tenth, if a = 4 and c = 10.
a2 + b2 = c2 (4)2 + b2 = (10)2 16 + b2 = 100 Solve for b. b2 = b2 = 84 b = 9.2 b

7 4. Find the length of the leg, to the nearest hundredth, if c = 10 and b = 7.
a2 + b2 = c2 a2 + (7)2 = (10)2 a = 100 Solve for a. a2 = a2 = 51 a = 7.1 c a b

8 a2 + b2 = c2 a2 + (3)2 = (15)2 a2 + 9 = 225 Solve for a. a2 = 225 - 9
Sample Problem: A 15 m ladder is propped against the side of a house. The base of the ladder is 3 m away from the house. How high up the wall does the ladder reach? a2 + b2 = c2 a2 + (3)2 = (15)2 a2 + 9 = 225 Solve for a. a2 = a2 = 216 a = 14.7 m c= 15 m a=? b= 3m


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