1. Oblique Triangles

2. Oblique Triangle – a non-right triangle.
It may be acute.
It may be obtuse.

3. We will label all our triangles the same way.
All triangles have six parts…three sides and three angles.
We will label all our triangles the same way.

4. A c b B a C

5. How you solve the oblique triangle depends on what you are given.
AAS
ASA
SSA
SSS
SAS

6. Decide whether the following are ASA, AAS, SSA, SSS, or SAS.
82
42 cm
65 cm
SAS

7. Decide whether the following are ASA, AAS, SSA, SSS, or SAS.
54
32 mm
ASA
37

8. Decide whether the following are ASA, AAS, SSA, SSS, or SAS.
14
AAS
22
19 miles

9. Decide whether the following are ASA, AAS, SSA, SSS, or SAS.
65
53 yd
SSA
87 yd

10. Law of Sines

11. Law of Sines a
sin A b
sin B c
sin C = = a c b A B C

12. Law of Sines
AAS
ASA
SSA

13. b sin B = sin C AAS c To find A: A = 180 – B – C To find c: b = c
Solve the following triangle:
C = 102.3, B = 28.7, and b = 27.4 feet
Step 1: Determine the Type of Triangle. C A B
Step 2: Determine which Law to use.
28.7
102.3
27.4 b
sin B = c
sin C
AAS
Step 3: Determine the missing parts.
To find A:
A = 180 – B – C
To find c:
b = c
sin B sin C
A = 180 – 102.3 – 28.7
= c
sin 28.7 sin 102.3
A = 49
c  sin 28.7 = 27.4  sin 102.3
c = 27.4  sin 102.3
sin 28.7
c = feet

14. To find a: a = b sin A sin B C = 102.3, B = 28.7, and b = 27.4 feet
c = feet
To find a:
a = b
sin A sin B
a =
sin 49 sin 28.7
a  sin 28.7 = 27.4  sin 49
a = 27.4  sin 49
sin 28.7
a = feet

15. A = 25, B = 35 , a = 3.5
Solve the Triangle.

16. ASA x Law of Sines Determine the height of the pole…
A pole tilts away from the sun at an 8 angle from vertical, and it casts a 22 foot shadow. The angle of elevation from the tip of the shadow to the top of the pole is 43. How tall is the pole?
Step 1: Determine the Type of Triangle. 8
22 feet
43
Step 2: Determine what part of the triangle you need to find.
Step 3: Determine which Law to use. x
Law of Sines
ASA
82
Determine the height of the pole…

17. Summary Use the Law of Sines Coming Tomorrow….. Law of Cosines
If the triangle is
AAS
ASA
SSA
Use the
Law of Sines
Coming Tomorrow…..
If the triangle is
SAS
SSS
Law of Cosines

18. One more thing….
Using SAS
To find
Area!!

19. Find the area of the triangle:
C = 8430’, a = 16 , and b = 20
Area = 1/2(side)(side) Sin < C A B
8430’ 16 20

20. Law of Cosines a2=b2+c2-2bc cosA b2=a2+c2-2ac cosB c2=a2+b2-2ab cosC a

21. Law of Cosines
SSS
SAS

22. Solve the triangle:
A = 40, b = 3 and c = 4

23. Solve the triangle:
a = 3, b = 5 and c = 7

24. A ship travels 60 miles due east, then adjust its course northward
A ship travels 60 miles due east, then adjust its course northward. After traveling 80 miles in that direction, the ship is 139 miles from the point of departure. Find the bearing from port to it’s new location.
The pitcher’s mound on a women’s softball field is 43 feet from home plate and the distance between the bases is 60 feet. How far is the pitcher’s mound from first base?

25. Summary Use the Law of Sines Use the Law of Cosines If the triangle is
AAS
ASA
SSA
Use the
Law of Sines
If the triangle is
SAS
SSS
Use the
Law of Cosines

26. Using SSS
To find
Area!!

27. Theorem Heron’s Formula
One more thing…
Theorem Heron’s Formula
The area A of a triangle with sides a, b, and c is

28. Find the area of a triangle whose sides are 5, 8, and 11.

29. C3B4ME