1. Radicals: Application and Problem Solving § 9.6

2. Angel, Elementary Algebra, 7ed 2 Pythagorean Theorem Revisited The square of the hypotenuse of a right triangle is equal to the sum of the squares of the two legs. (leg) 2 + (leg) 2 = (hypotenuse) 2 a 2 + b 2 = c 2 If a and b represent the legs, and c represents the hypotenuse, then a b c a

3. Angel, Elementary Algebra, 7ed 3 Pythagorean Theorem Revisited A local cable company must run a guy wire to support a pole. The wire will go from the top of a 14-meter pole to a point 6 meters from the base of the pole. How long will the guy wire be? 14 m 6 m ? m Example: The base of the pole and the ground form a right angle, so the Pythagorean Theorem may be used. Continued.

4. Angel, Elementary Algebra, 7ed 4 14 m 6 m ? m Let a be the pole length, a = 14 Let b be the ground from the pole to the wire, b = 6 Let c be the length of the wire, c = ? a 2 + b 2 = c 2 14 2 + 6 2 = c 2 196 + 36 = c 2 232 = c 2 The length of the wire is 15.23 meters Pythagorean Theorem Revisited Example continued:

5. Angel, Elementary Algebra, 7ed 5 Distance Formula The distance formula can be used to find the distance between two points (x 1, y 1 ) and (x 2, y 2 ). (4, -3) (-5, 6) The two points in the diagram are (-5, 6) and (4, -3). It makes no difference which point is labeled (x 1, y 1 ) and (x 2, y 2 ).

6. Angel, Elementary Algebra, 7ed 6 Distance Formula (4, -3) (-5, 6) 12.73 units