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Chapter 7 Lesson 3. Objective: To use the properties of 30°-60°-90° triangle. 30°. 30°. 60°. 60°. Theorem 7-9: 30°-60°-90° Triangle Theorem

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chapter 7 lesson 3

Chapter 7 Lesson 3

Objective: To use the properties of 30°-60°-90° triangle.

slide2

30°

30°

60°

60°

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

hypotenuse

long leg

2x

x√3

short leg

x

example 1 finding the lengths of the legs

60°

8

x

30°

y

Example 1:Finding 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 = √3 • shorter leg

y = x√3

y = 4√3

example 2 finding the lengths of the legs

60°

12

x

30°

y

Example 2:Finding 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 = √3 • shorter leg

y = x√3

y = 6√3

example 3 finding the lengths of the legs

60°

4√3

x

30°

y

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

Longer Leg

longer leg = √3 • shorter leg

y = x√3

y = 2√3•√3

Y=6

slide6

30°

60°

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

x

y

slide7

30°

60°

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

√6

y

slide8

30°

60°

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

x

y

homework
Homework

Page 369 – 371

#12-22; 24-27; 30-33; 35;38