1. SOLVING FOR THE MISSING PART OF AN OBLIQUE TRIANGLE
LAW OF SINES
SOLVING FOR THE MISSING PART OF AN OBLIQUE TRIANGLE

2. An oblique triangle is a triangle that has no right angles.C B A a b c
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.

3. The following cases are considered when solving oblique triangles.
Two angles and any side (AAS or ASA)
2. Two sides and an angle opposite one of them (SSA) C c a a c b
3. Three sides (SSS) 3 c a B
4. Two sides and their included angle (SAS)

4. If ABC is an oblique triangle with sides a, b, and c, then
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 C B A b h c a C B A b h c a
Acute Triangle
Obtuse Triangle

5. The Law of Sines
Use when the
given info is…
ASA or AAS.

6. The Law of Sines Start by solving Solve ∆ABC if A = 42º,
for the missing angle.
Solve ∆ABC if A = 42º,
b = 6.4, and C = 81º.
B = 180º - 42º - 81º
B = 57º

7. The Law of Sines Solve ∆ABC if A = 42º, b = 6.4, and C = 81º.
Then solve for one of
the missing sides.

8. The Law of Sines Solve ∆ABC if A = 42º, b = 6.4, and C = 81º.
Finally solve for the
remaining side.

9. Example (SSA): Use the Law of Sines to solve the triangle.
A = 110°, a = 125 inches, b = 100 inches C B A
b = 100 in c
a = 125 in
110°
21.26°
48.74°
48.23 in
C ≈ 180° – 110° – 48.74°
= 21.26°

10. Use the Law of Sines to find side b and c.
Example (ASA):
Find the remaining angle and sides of the triangle. C B A b c
60°
10°
a = 4.5 ft
The third angle in the triangle is A = 180° – A – B
= 180° – 10° – 60°
= 110°.
4.15 ft
110°
0.83 ft
Use the Law of Sines to find side b and c.

11. Now, you try some! Solve these triangles. A = 40° B = 20° a = 2
Always draw your triangle before you use the Sine Law
Now, you try some!
Solve these triangles.
A = 40° B = 20° a = 2
A = 110° C = 30° c = 3
3) A = 30° b = C = 50°
4) c = 2 A = 40° B = 40°