G 8 2 Special Right Triangles 1 4590

G. 8. 2 Special Right Triangles 1

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

30°-60°-90° Special Right Triangle l 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 Long Leg a 2 a 60° a Short Leg Special Right Triangles 3

30°-60°-90° Special Right Triangle l 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° 5 60° cm 10 cm 60° X Longer Leg X 2 X Shorter Leg Special Right Triangles 5 cm 4

Example: Find the value of a and b. 7 cm b = 14 cm 60° 30° 2 x b a= cm 60° 30 ° 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 = 2 x, and a = x Step 5: Solve for a and b Special Right Triangles 5 .

Example: Find the value of a and b. 7 cm b=7 45° cm 45° b x 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°-90° Step 3: Match the 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 6 .