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Special Right Triangles 1 G.8.2 Special Right Triangles

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2 45°-45°-90° Special Right Triangle In a triangle 45°-45°-90°, the hypotenuse is times as long as a leg. 45° Hypotenuse X X X Leg Example: 45° 5 cm 5 cm

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Special Right Triangles 3 30°-60°-90° Special Right Triangle In a 30°-60°-90° triangle, the hypotenuse is twice as long as the short leg, and the long leg is times as long as the shorter leg. 60° 30° Hypotenuse a 2a Long Leg Short Leg a

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Special Right Triangles 4 30°-60°-90° Special Right Triangle In a triangle 30°-60°-90°, the hypotenuse is twice as long as the shorter leg, and the longer leg is times as long as the shorter leg. 30° 60° Hypotenuse X 2X X Longer Leg Shorter Leg Example: 30° 60° 10 cm 5 cm

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Special Right Triangles 5 Example: Find the value of a and b. 60° 7 cm a b Step 1: Find the missing angle measure.30° Step 2: Decide which special right triangle applies.30°-60°-90° Step 3: Match the 30°-60°-90° pattern with the problem. 30° 60° x 2x a = cm b = 14 cm Step 5: Solve for a and b Step 4: From the pattern, we know that x = 7, b = 2x, and a = x.

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Special Right Triangles 6 Example: Find the value of a and b. 45° 7 cm a b Step 1: Find the missing angle measure.45° Step 2: Decide which special right triangle applies.45°-45°-90° Step 3: Match the 45°-45°-90° pattern with the problem. 45° x x x Step 4: From the pattern, we know that x = 7, a = x, and b = x. a = 7 cm b = 7 cm Step 5: Solve for a and b

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