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

2. 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

3. 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

4. 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

5. 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

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

7. 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

8. 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

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