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Toothpicks and PowerPoint. Ambiguous Case of the Law of Sines. Pam Burke Potosi High School #1 Trojan Drive Potosi, MO 63664 573-438-2156 pburke@potosir3.org pamburke74@gmail.com . To solve a right triangle, you can use the Pythagorean Theorem and/or basic trig ratios. A. c. b.

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Toothpicks

and

PowerPoint

Ambiguous Case

of the

Law of Sines

Pam Burke

Potosi High School

#1 Trojan Drive

Potosi, MO 63664

573-438-2156

pburke@potosir3.org

pamburke74@gmail.com

To solve a right triangle, you can

use the Pythagorean Theorem

and/or basic trig ratios.

A

c

b

B

C

a

In an oblique triangle (one in which

there are no right angles) neither of

those methods will work.

Solving an oblique triangle requires

using either the Law of Sines or

the Law of Cosines, depending on

which information you are given.

In this lesson we

are going to use

the Law of Sines.

The Law of Sines can be used

when you are given two angles

and one side of an oblique triangle

(ASA or AAS).

Here is an example. You are given

two angles and one side of a triangle.

Find the measures of the other angle

and the other two sides.

C

b

A

a

c

B

A = 65º a = 28

B = 32º b = ?

C = ? c = ?

C

b

A

a

A = 65º a = 28

B = 32º b = ?

C = ? c = ?

c

B

C = 180º - (A + B) = 180º - (65 + 32)

= 180º - 97º = 83º

C

b

A

a

A = 65º a = 28

B = 32º b = ?

C = 83º c = ?

c

B

C

b

A

a

A = 65º a = 28

B = 32º b ≈16.4

C = 83º c = ?

c

B

Now you have solved the triangle;

you know the measures of all

three sides and all three angles.

C

b

A

a

c

B

A = 65º a = 28

B = 32º b ≈16.4

C = 83º c ≈ 30.7

The Law of Sines can also be

used to solve an oblique triangle

when you are given two sides

and the angle opposite one of

the sides (SSA).

A

a

b

Suppose you are given the

measures shown below for

two sides and an angle of

an oblique triangle.

b

a

A

The pieces could be put

together to form this

triangle.

b

a

A

But they could also

be put together to

form this triangle.

b

b

a

a

A

A

Since SSA does not always

define a unique triangle, this

is called the Ambiguous Case

of the Law of Sines.