1. Essential question: How do I solve oblique triangles?
How do I use Law Of Sines – AAS, ASA, & 1st case of SSA to solve oblique triangles?

2. To “solve a triangle” is to find…
CAPITAL LETTERS ARE ANGLES
lower cased letters are sides
To “solve a triangle” is to find…
the lengths of all sides and… the measures of all angles. A C B a b c

3. ...are triangles that have no right angles.
Oblique Triangles
...are triangles that have no right angles. A C B a b c

4. To solve an oblique triangle you need to know
To solve an oblique triangle you need to know... at least one side and two other parts of the triangle.
1) two angles and any side (ASA or AAS)
2) two sides and an angle opposite one of them (SSA)
3) three sides (SSS) learned yesterday
4) two sides and their included angle (SAS) learned yesterday

5. Law of Sines A C B a b c
AAS
ASA

6. Ex. Solve ABC, B=64°, C= 38° and b=9ft

7. Ex. 1
Solve ABC.
C = 102.3°, B = 28.7°, and b = 27.4 feet C
AAS
A =
49º a
a =
43.06 ft b
B = 28.7º
b = 27.4 ft B A c
C = 102.3º
c =
55.75 ft
A = 180º º º
= 49º

8. ASA Ex. 2 C = 180º - 43º - 98º Solve the triangle. A = 43° a =
23.84 ft C
ASA
B = 98º
b =
34.62 ft b
C =
39º
c = 22 ft a
98°
43°
22 feet
C = 180º - 43º - 98º
= 39º

9. Ex. 7
The course for a boat race starts at point A and proceeds in the direction S52°W to point B, then in the direction S40°E to point C, and finally back to A. Approximate the total distance of the race course.
40°
52°
8 km A B C D
The length of the race course will be a + b + c
B = 180º – 40º – 52º
The length of the race course will be km
= 88º
40°
a = 6.31
c = 5.15

10. When did we have problems proving triangles congruent?
When we had SSA.
It is still a problem. When we have SSA, we can have no triangle that exist, we can have 1 triangle, or we can have 2 triangles.
Let’s look….

11. SSA Ex. 4 Solve the triangle. A = 85° a = 15 ft B = b = 25 ft C = c =
25 feet
No triangle exists.

12. What are your questions?