7.1 Applying the Pythagorean Theorem

1. 7.1 Applying the Pythagorean Theorem

2. Things to remember: • Formula: a2+b2=c2 • Pythagorean Theorem is used to find lengths of the sides of a right triangle • Side across from the right angle is called the hypotenuse and is always “c” c

3. Pythagorean Triples and Multiples Most common Pythagorean triples are across the top row. The other triples are the result of multiplying each integer in the top row by the same factor.

4. Example 1 • Find the length of the hypotenuse of the right triangle. 48 m 36 m a = = b (48)2 + (36)2 = x2 2304 + 1296 = x2 c = x 3600 = x2 60 m = x

5. Example 2 • Find the unknown leg length x. (4.9)2 + (x)2 = (5.7)2 c = 5.7 ft 24.01 + x2 = 32.49 4.9 ft a = -24.01 -24.01 x2 = 8.48 b = x x = 2.9 ft

6. Example 3 • Find the area of the isosceles triangle Remember area of a triangle is A = ½ bh 17 c = a = 16/2 = 8 b = h First find h. Last find Area Base (b) = 16 m (8)2 + (h)2 = (17)2 Height (h)= 15 m 64 + h2 = 289 -64 -64 A = ½ (16)(15) A = 120 m h2 = 225 h = 15 m

7. Example 4 • Find the unknown side length x. Write your answer in simplest radical form. First what information is missing? 5 c = Find y. Now Find x. a = 3 (4)2 + (7)2 = (x)2 b = y 16 + 49= x2 This is a Pythagorean Triple! This side is missing! 65 = x2 So y = 4 We’ll call it y x = ft

8. Assignment Section 7.1 Pg 436; 1, 4-17, 24-27, 39-45, 49-50 Give answers in simplified radical form if they do not come out to whole numbers.