Transcript Chapter 7 Lesson 3 - Mrs.Lemons Geometry

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
30°
long leg
x√3
longer leg = √3 • shorter leg
30°
60°
60°
x
short leg
Example 1:
Finding the Lengths of the Legs
Find the value of each variable.
Shorter Leg
8
60°
x
hypotenuse = 2 • shorter leg
30°
y
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.
12
60°
x
30°
y
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
4√3
60°
x
30°
y
hypotenuse = 2 • shorter leg
4√3 = 2x
x = 2√3
Longer Leg
longer leg = √3 • shorter leg
y = x√3
y = 2√3•√3
Example 4:
Using the Length of a Leg
Find the value of each variable.
Shorter Leg
5
long leg = √3 • short leg
30°
y
60°
5x 3
x
5
3
x 

3
3
5 3
x 
3
Hypotenuse
Hyp. = 2 • shorter leg
y  2x
5 3
y  2
3
10 3
y 
3
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
Hypotenuse
hyp. = 2 • shorter leg
longer leg = √3 • shorter leg
x
30°
y
√6
60°
x  3 6
y  2x
x  18
y  2 6
x  92
y 2 6
x 3 2
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
18
30°
y
x
60°
18  3  x
18
x 
3
18
3
x 

3
3
18 3
x 
3
x 6 3
Hypotenuse
hyp. = 2 • shorter leg
y  26 3
y  12 3
Homework
Page 369 – 371
#12-22; 24-27; 30-33; 35;38