Oblique Triangles l Oblique Triangle a nonright triangle

Oblique Triangles

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

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

A c b B a C

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

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

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

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

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

Law of Sines

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

Law of Sines l AAS l ASA l SSA

Solve the following triangle: C = 102. 3 , B = 28. 7 , and b = 27. 4 feet Step 1: Determine the Type of Triangle. Step 2: Determine which Law to use. 102. 3 27. 4 AAS 28. 7 b = c sin B sin C Step 3: Determine the missing parts. To find A: A = 180 – B – C A = 180 – 102. 3 – 28. 7 A = 49 To find c: b = c sin B sin C 27. 4 = sin 28. 7 c sin 102. 3 c sin 28. 7 = 27. 4 sin 102. 3 c = 27. 4 sin 102. 3 sin 28. 7 c = 55. 75 feet

C = 102. 3 , B = 28. 7 , and b = 27. 4 feet C 102. 3 27. 4 28. 7 A = 49 B c = 55. 75 feet To find a: A a = b sin A sin B a = 27. 4 sin 49 sin 28. 7 a sin 28. 7 = 27. 4 sin 49 a = 27. 4 sin 49 sin 28. 7 a = 43. 06 feet

A = 25 , B = 35 , a = 3. 5 Solve the Triangle.

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. Step 2: Determine what part of the triangle you need to find. Step 3: Determine which Law to use. 8 Law of Sines x 82 ASA 22 feet 43 Determine the height of the pole…

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

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

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

Law of Cosines a 2=b 2+c 2 -2 bc cos. A b 2=a 2+c 2 -2 ac cos. B c 2=a 2+b 2 -2 ab cos. C B c a C b A

Law of Cosines l SSS l SAS

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

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

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?