Oblique TrianglesOblique Triangles

Oblique Triangle – a non-right triangle.Oblique Triangle – a non-right triangle.

It may be acute.It may be acute.

It may be obtuse.It may be obtuse.

We will label all our triangles the same way.We will label all our triangles the same way.

All triangles have six parts…three All triangles have six parts…three sides and three angles.sides and three angles.

A

a

B

b

C

c

Law of SinesLaw of SinesUsed when you have an Used when you have an

angle/side pair.angle/side pair.

Law of SinesLaw of Sines

a

sin A=

b

sin B=

c

sin C

a

c

bA

B

C

28.7102.3

27.4

Solve the following triangle:

C = 102.3, 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.

bsin B

= c sin C

Step 3: Determine the missing parts.To find A:A = 180 – B – CA = 180 – 102.3 – 28.7A = 49

To find c: b = c sin B sin C 27.4 = csin 28.7 sin 102.3

c sin 28.7 = 27.4 sin 102.3

c = 27.4 sin 102.3 sin 28.7c = 55.75 feet

C = 102.3, B = 28.7, and b = 27.4 feet

C

A

B A = 49

c = 55.75 feet

To find a:

a = b sin A sin B

a = 27.4sin 49 sin 28.7

a sin 28.7 = 27.4 sin 49 a = 27.4 sin 49

sin 28.7

102.328.727.4

a = 43.06 feet

A = 25, B = 35 , a = 3.5Solve 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

22 feet43

Step 2: Determine what part of the triangle you need to find.

xStep 3: Determine which Law to use.

Law of Sines

Determine the height of the pole…

Law of CosinesLaw of CosinesUsed when you do NOT have Used when you do NOT have

an angle/side pair.an angle/side pair.

Law of CosinesLaw of Cosines

C

c

B

b

A

a

sinsinsin

a2=b2+c2-2bc cosA

b2=a2+c2-2ac cosB

c2=a2+b2-2ab cosC

a

c

bA

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.

SummaryIf the triangle has an angle/side matching

pair, use the:

If the triangle has an angle/side matching

pair, use the:

Law of Sines

Law of Cosines