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**Special Right Triangles**

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**45°-45°-90° Special Right Triangle**

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

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**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. 30° Hypotenuse 2a Long Leg a 60° a Short Leg Special Right Triangles

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**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. Example: Hypotenuse 30° 2X Longer Leg 30° 10 cm X cm 60° 60° X 5 cm Shorter Leg Special Right Triangles

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**Example: Find the value of a and b.**

b = 14 cm 60° 7 cm 30° 2x b 30 ° 60° a = cm a x 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. Step 4: From the pattern, we know that x = 7 , b = 2x, and a = x . Step 5: Solve for a and b Special Right Triangles

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**Example: Find the value of a and b.**

b = cm 45° 7 cm 45° x b x 45 ° 45° a = 7 cm a x 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. Step 4: From the pattern, we know that x = 7 , a = x, and b = x . Step 5: Solve for a and b Special Right Triangles

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