Chapter%207%20Lesson%203

1
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 v3 times the
length of the shorter leg. hypotenuse 2
shorter leg longer leg v3 shorter leg
hypotenuse
long leg
2x
xv3
short leg
x
3
Example 1Finding the Lengths of the Legs
Find the value of each variable.
Shorter Leg hypotenuse 2 shorter leg 8 2x x
4
Longer Leg longer leg v3 shorter leg y
xv3 y 4v3
4
Example 2Finding the Lengths of the Legs
Find the lengths of a 30-60-90 triangle with
hypotenuse of length 12.
Shorter Leg hypotenuse 2 shorter leg 12
2x x 6
Longer Leg longer leg v3 shorter leg y
xv3 y 6v3
5
Example 3Finding the Lengths of the Legs
Find the lengths of a 30-60-90 triangle with
hypotenuse of length 4v3.
Shorter Leg hypotenuse 2 shorter leg 4v3
2x x 2v3
Longer Leg longer leg v3 shorter leg y
xv3 y 2v3v3 Y6
6
Example 4Using the Length of a Leg
Find the value of each variable.
Shorter Leg long leg v3 short leg
Hypotenuse Hyp. 2 shorter leg
5
x
y
7
Example 5Using the Length of a Leg
The shorter leg of a 30-60-90 has length v6.
What are the lengths of the other sides? Leave
your answers in simplest radical form.
Longer Leg longer leg v3 shorter leg
Hypotenuse hyp. 2 shorter leg
x
v6
y
8
Example 6Using 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 v3 short leg
Hypotenuse hyp. 2 shorter leg
18
x
y
9
Homework
Page 369 371 12-22 24-27 30-33 3538