Oblique Triangles

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

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

A a B b C c

Law of Sines Used when you have an angle/side pair.

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

C A B 28.7   27.4 Solve the following triangle: C = , B = 28.7 , and b = 27.4 feet Step 1: Determine whether or not you have a angle/side pair. Step 2: Determine which Law to use. b sin B = c sin C Step 3: Determine the missing parts. To find A: A = 180  – B – C A = 180  –  – 28.7  A = 49  To find c: b = c sin B sin C 27.4 = c sin 28.7  sin  c  sin 28.7  = 27.4  sin  c = 27.4  sin  sin 28.7  c = feet

C = , B = 28.7 , and b = 27.4 feet C A B A = 49  c = feet To find 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   28.7  27.4 a = 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. 82  88 22 feet 43  Step 2: Determine what part of the triangle you need to find. x Step 3: Determine which Law to use. Law of Sines Determine the height of the pole…

Law of Cosines Used when you do NOT have an angle/side pair.

Law of Cosines a 2 =b 2 +c 2 -2bc cosA b 2 =a 2 +c 2 -2ac cosB c 2 =a 2 +b 2 -2ab cosC a c b A B C

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.

Summary If the triangle has an angle/side matching pair, use the: Law of Sines Law of Cosines