EQ: What is the law of sines, and how can we use it to solve right triangles?

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EQ: What is the law of sines, and how can we use it to solve right triangles?

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EQ: What is the law of sines, and how can we use it to solve right triangles?

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EQ: What is the law of sines, and how can we use it to solve right triangles?

EQ: What is the law of sines, and how can we use it to solve right triangles?

The Law of Sines allows you to solve a triangle as long as you know either of the following:

1. Two angle measures and any side length–angle-angle-side (AAS) or angle-side-angle (ASA) information

2. Two side lengths and the measure of an angle that is not between them–side-side-angle (SSA) information

EQ: What is the law of sines, and how can we use it to solve right triangles?

Using the Law of Sines for AAS and ASA

Solve the triangle. Round to the nearest tenth.

Step 1. Find the third angle measure.

mD + mE + mF = 180°

Triangle Sum Theorem.

Substitute 33° for mD and 28° for mF.

33° + mE + 28° = 180°

mE = 119°

Solve for mE.

sin F

sin D

sin F

sin E

=

=

d

e

f

f

sin 28°

sin 28°

sin 119°

sin 33°

=

=

e

d

15

15

15 sin 33°

15 sin 119°

d =

e =

sin 28°

sin 28°

d ≈ 17.4

e ≈ 27.9

EQ: What is the law of sines, and how can we use it to solve right triangles?

Step 2 Find the unknown side lengths.

Law of Sines.

Substitute.

Cross

multiply.

e sin 28° = 15 sin 119°

d sin 28° = 15 sin 33°

Solve for the

unknown side.

r

Q

EQ: What is the law of sines, and how can we use it to solve right triangles?

Using the Law of Sines for AAS and ASA

Solve the triangle. Round to the nearest tenth.

Step 1 Find the third angle measure.

Triangle Sum Theorem

mP = 180° – 36° – 39° = 105°

10 sin 36°

10 sin 39°

q=

r=

≈ 6.1

≈ 6.5

sin 105°

sin 105°

r

Q

sin Q

sin R

sin P

sin P

=

=

p

q

p

r

sin 39°

sin 36°

sin 105°

sin 105°

=

=

r

q

10

10

EQ: What is the law of sines, and how can we use it to solve right triangles?

Solve the triangle. Round to the nearest tenth.

Step 2 Find the unknown side lengths.

Law of Sines.

Substitute.

EQ: What is the law of sines, and how can we use it to solve right triangles?

Solve the triangle. Round to the nearest tenth.

Step 1 Find the third angle measure.

mH + mJ + mK = 180°

Substitute 42° for mH and 107° for mJ.

42° + 107° + mK = 180°

mK = 31°

Solve for mK.

sin J

sin H

sin H

sin K

=

=

h

k

h

j

sin 42°

sin 107°

sin 31°

sin 42°

=

=

k

h

8.4

12

12 sin 42°

8.4 sin 31°

h =

k =

sin 107°

sin 42°

h ≈ 8.4

k ≈ 6.5

EQ: What is the law of sines, and how can we use it to solve right triangles?

Step 2 Find the unknown side lengths.

Law of Sines.

Substitute.

Cross

multiply.

8.4 sin 31° = k sin 42°

h sin 107° = 12 sin 42°

Solve for the

unknown side.

EQ: What is the law of sines, and how can we use it to solve right triangles?

Solve the triangle. Round to the nearest tenth.

Step 1 Find the third angle measure.

Triangle Sum Theorem

mN = 180° – 56° – 106° = 18°

sin M

sin P

sin N

sin M

=

=

sin 56°

sin 106°

n

m

m

p

=

p

4.7

sin 106°

sin 18°

1.5 sin 106°

4.7 sin 56°

=

m=

p=

≈ 4.7

≈ 4.0

m

1.5

sin 18°

sin 106°

EQ: What is the law of sines, and how can we use it to solve right triangles?

Solve the triangle. Round to the nearest tenth.

Step 2 Find the unknown side lengths.

Law of Sines.

Substitute.