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§ 7.6

§ 7.6. The Pythagorean Theorem. Hypotenuse. Leg. Leg. 5. 3. 4. Pythagorean Theorem. The Pythagorean Theorem states that the square of the hypotenuse of a right triangle equals the sum of the squares of the two legs. (hypotenuse) 2 = (leg) 2 + (leg) 2 . 5 2 = 3 2 + 4 2.

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§ 7.6

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  1. § 7.6 The Pythagorean Theorem

  2. Hypotenuse Leg Leg 5 3 4 Pythagorean Theorem The Pythagorean Theorem states that the square of the hypotenuse of a right triangle equals the sum of the squares of the two legs. (hypotenuse)2 = (leg)2 + (leg)2 52 = 32 + 42 25 = 9 + 16 25 = 25 

  3. hypotenuse 8 14 Finding the Hypotenuse Example: Find the hypotenuse of a right triangle with legs of 14 yd and 8 yd.

  4. 15 cm leg 11 cm Finding the Length of a Leg The missing length of a leg can be found when the length of the hypotenuse and the other leg is known. Example: Find the length of the leg in the triangle.

  5. 2 3 start Applied Problems Example: Joe runs out of gas in Plainsville, Indiana. He walks 3 miles north and then 2 miles east looking for gas. How far is he from his staring point? Joe is approximately 3.61 miles from his staring point.

  6. 60° 60° 30° 30° 30°–60°–90° Triangles 12 in 6 in In a 30°–60°–90° triangle, the length of the leg opposite the 30° angle is  the length of the hypotenuse. 9 ft 4.5 ft

  7. 45° In a 45°–45°–90° triangle, the lengths of the sides opposite the 45° angles are equal. The length of the hypotenuse is equal to  the length of either leg. 45°  1.414 Hypotenuse =  6 45°–45°–90° Triangles 8.5 in 6 in 6 in  1.414  6  8.49

  8. 24 ft 45° y 45° x Hypotenuse =  x 45°–45°–90° Triangles Example: Find the length of sides x and y.  17.0 ft  17.0 ft Side x is equal to approximately 17.0 feet, therefore side y is also equal to approximately 17.0 feet.

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