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Right Triangles And the Pythagorean Theorem

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Legs of a Right Triangle Leg -the two sides of a right triangle that form the right angle Leg

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Hypotenuse In a right triangle, the side opposite the right angle is the hypotenuse.

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Triangle The sum of all angles measure 180° in a triangle. A right triangle has a 90° angle.

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Pythagorean Theorem The Pythagorean Theorem is used to find the measure of an unknown side of a right triangle. The Pythagorean Theorem is used to find the measure of an unknown side of a right triangle. Legs are side a and side b. Hypotenuse is side c. The Pythagorean Theorem: a² + b² = c²

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Pythagorean Theorem The legs of a right triangle measure 6 in. and 8 in. What does the hypotenuse measure? a² + b² = c² 6² + 8² = c² 36 + 64 = c² 100 = c² √100 = √c² 10 = c The hypotenuse is 10 in.

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Practice Problem a² + b² = c² 3² + 4² = c² 9 + 16 = c² 25 = c² √25 = √c² 5 = c 3 cm 4 cm C

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Pythagorean Theorem a² + b² = c² 9² + b² = 15² 81 + b² = 225 -81 -81 b² = 144 √b² = √144 b = 12 To find the measurement of a leg, we use the Pythagorean Theorem with leg a or b and the hypotenuse.

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Practice Problems a² + b² = c² 12² + b² = 13² 144 + b² = 169 -144 -144 b² = 25 √b² = √25 b = 5 12 mm 13 mm b 18 cm 30 cm a a² + b² = c² a² + 18² = == = 30² a² + 324 = 900 -324 -324 a² = 576 √a² = √576 a = 24

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Pythagorean Theorem Review a² + b² = c² Leg a and leg b represent the sides of the right triangle. Side c is the hypotenuse of a right triangle.

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Finding the Hypotenuse a² + b² = c² a² + b² = c² 7² + 10² = c² 7² + 10² = c² 49 + 100 = c² 49 + 100 = c² 149 = c² 149 = c² √149 = √c² √149 = √c² 12.2 ≈ c 12.2 ≈ c

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Pythagorean Theorem What is the diagonal length of a TV screen whose dimensions are 80 x 60 cm? a² + b² = c² 80² + 60² = c² 6,400 + 3,600 = c² 10,000 = c² √10,000 = √c² 100 = c The diagonal length of the TV screen is 100 cm.

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Finding the Leg of a Right Triangle a² + b² = c² 11² + b² = 18² 121 + b² = 324 -121 -121 b² = 203 √b² =√203 b ≈ 14.2

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Pythagorean Theorem How far up a wall will an 11m ladder reach, if the foot of the ladder must be 4m from the base of the wall? a² + b² = c² 4² + b² = 11² 16 + b² = 121 -16 -16 b² = 105 √b² =√105 b ≈ 10.2 The ladder will reach 10.2 meters up the wall.

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