7.1 Apply the Pythagorean Theorem

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7.1 Apply the Pythagorean Theorem Hubarth Geometry

Pythagorean Theorem B c a A C b

Ex 1. Find the length of the Hypotenuse 12 5 c Solution Hypotenuse = 13

Subtract 16 from each side. Ex 2 Standardized Test Practice = + 162 = 42 + x2 Substitute. 256 = 16 + x2 Multiply. 240 = x2 Subtract 16 from each side. 240 = x Find positive square root. 15.491 ≈ x Approximate with a calculator.

Subtract 25 from each side. Ex 3 Find the Area of an Isosceles Triangle Find the area of the isosceles triangle with side lengths 10 meters, 13 meters, and 13 meters. c2 = a2 + b2 Pythagorean Theorem 132 = 52 + h2 Substitute. 169 = 25 + h2 Multiply. 144 = h2 Subtract 25 from each side. 12 = h Find the positive square root. Find the area. 1 2 (base) (height) = (10) (12) = 60 m2 1 2 Area =

Ex 4 Find the unknown side length of the right triangle b 7 14

Find the unknown side length Practice Find the unknown side length 1. 2. 8 10 7 6 c a 3. Find the area of the triangle. about 149.2 ft2.