LAW OF SINESSOLVING FOR THE MISSING PART OF AN OBLIQUE

TRIANGLE

An oblique triangle is a triangle that has no right angles.

To solve an oblique triangle, you need to know the measure of at least one side and the measures of any other two parts of the triangle – two sides, two angles, or one angle and one side.

C

BA

ab

c

3

The following cases are considered when solving oblique triangles.

1.Two angles and any side (AAS or ASA)

2. Two sides and an angle opposite one of them (SSA)

3. Three sides (SSS)

4. Two sides and their included angle (SAS)

A

C

cA

B

c

a

cb

C

c

a

c

aB

The first two cases can be solved using the Law of Sines. (The last two cases can be solved using the Law of Cosines.)

Law of Sines

If ABC is an oblique triangle with sides a, b, and c, then

Acute Triangle

C

BA

bh

c

a

C

BA

bh

c

a

Obtuse Triangle

The Law of Sines

Use when the given info is… ASA or AAS.

The Law of SinesSolve ∆ABC if A = 42º, b = 6.4, and C = 81º.

Start by solving for the missing angle.

B = 180º - 42º - 81º

B = 57º

The Law of SinesSolve ∆ABC if A = 42º, b = 6.4, and C = 81º.

Then solve for one ofthe missing sides.

The Law of SinesSolve ∆ABC if A = 42º, b = 6.4, and C = 81º.

Finally solve for theremaining side.

Use the Law of Sines to solve the triangle.A = 110, a = 125 inches, b = 100 inches

Example (SSA):

C ≈ 180 – 110 – 48.74

C

BA

b = 100 in

c

a = 125 in

110 48.74

21.26

48.23 in

= 21.26

Find the remaining angle and sides of the triangle.

Example (ASA):

The third angle in the triangle is A = 180 – A – B = 180 – 10 – 60 = 110.

C

BA

b

c

60

10

a = 4.5 ft

110

Use the Law of Sines to find side b and c.

4.15 ft

0.83 ft

Now, you try some!Now, you try some!

Solve these triangles.

• A = 40° B = 20° a = 2

1)A = 110° C = 30° c = 3

3) A = 30° b = 10 C = 50°

4) c = 2 A = 40° B = 40°

Always draw your triangle before you use the Sine Law