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Lesson 7-3

Lesson 7-3. Special Right Triangles. 45°-45°-90° Special Right Triangle. In a triangle 45°-45°-90° , the hypotenuse is times as long as a leg. Example:. 45°. 45°. 5 cm. Hypotenuse. 5 cm. Leg. X. X. 45°. 5 cm. 45°. Leg. X. X. 5 cm.

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Lesson 7-3

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  1. Lesson 7-3 Special Right Triangles Lesson 7-3: Special Right Triangles

  2. 45°-45°-90° Special Right Triangle • In a triangle 45°-45°-90° , the hypotenuse is times as long as a leg. Example: 45° 45° 5 cm Hypotenuse 5 cm Leg X X 45° 5 cm 45° Leg X Lesson 7-3: Special Right Triangles

  3. X 5 cm 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 60° 60° X Shorter Leg 5 cm Lesson 7-3: Special Right Triangles

  4. Step 4: From the pattern, we know that x = 7 , b = 2x, and a = x . 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 5: Solve for a and b Lesson 7-3: Special Right Triangles

  5. Example: Find the value of a and b. b = 7 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 Lesson 7-3: Special Right Triangles

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