Lesson 7 3 Special Right Triangles Lesson 7

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

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

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 Lesson 7 -3: Special Right Triangles 3

l In a 30°-60°-90°Special triangle, Right the hypotenuse is twice as long as the short 30°-60°-90° Triangle leg, and the long leg is times as long as the shorter leg. 30° Long Leg a Hypotenuse 2 a 60° a Special Right Short Leg. Lesson 7 -3: Triangles 4

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° 2 X Longer Leg X 30° 5 cm 10 cm 60° Shorter Leg Lesson 7 -3: Special Right Triangles 60° 5 cm 5 X

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 Lesson 7 -3: Special Right Triangles 6 .

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 Lesson 7 -3: Special Right Triangles 7 .