Objective: To use the properties of 30°-60°-90° triangle. Chapter 7 Lesson 3 Objective: To use the properties of 30°-60°-90° triangle.

Theorem 7-9: 30°-60°-90° Triangle Theorem In a 30°-60°-90° triangle, the length of the hypotenuse is twice the length of the shorter leg. The length of the longer leg is √3 times the length of the shorter leg. hypotenuse = 2 • shorter leg longer leg = √3 • shorter leg 30° 60° 30° 60° long leg hypotenuse 2x x√3 short leg x

Example 1: Finding the Lengths of the Legs Find the value of each variable. 60° 30° x y 8 Shorter Leg hypotenuse = 2 • shorter leg 8 = 2x x = 4 Longer Leg longer leg = √3 • shorter leg y = x√3 y = 4√3

Example 2: Finding the Lengths of the Legs Find the lengths of a 30°-60°-90° triangle with hypotenuse of length 12. 60° 30° y x 12 Shorter Leg hypotenuse = 2 • shorter leg 12 = 2x x = 6 Longer Leg longer leg = √3 • shorter leg y = x√3 y = 6√3

Example 3: Finding the Lengths of the Legs Find the lengths of a 30°-60°-90° triangle with hypotenuse of length 4√3. Shorter Leg hypotenuse = 2 • shorter leg 4√3 = 2x x = 2√3 60° 30° x y 4√3 Longer Leg longer leg = √3 • shorter leg y = x√3 y = 2√3•√3 Y=6

Example 4: Using the Length of a Leg Find the value of each variable. Shorter Leg long leg = √3 • short leg Hypotenuse Hyp. = 2 • shorter leg 5 30° 60° x y

Example 5: Using the Length of a Leg The shorter leg of a 30°-60°-90° has length √6. What are the lengths of the other sides? Leave your answers in simplest radical form. Longer Leg longer leg = √3 • shorter leg Hypotenuse hyp. = 2 • shorter leg x 30° 60° √6 y

Example 6: Using the Length of a Leg The longer leg of a 30°-60°-90° has length 18. Find the length of the shorter leg and the hypotenuse. Shorter Leg long leg = √3 • short leg Hypotenuse hyp. = 2 • shorter leg 18 30° 60° x y

Homework Page 369 – 371 #12-22; 24-27; 30-33; 35;38