Oblique TrianglesOblique Triangles

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

How you solve the oblique triangle How you solve the oblique triangle depends on what you are given.depends on what you are given.

AASAASASAASASSASSASSSSSSSASSAS

Decide whether the following are Decide whether the following are ASA, AAS, SSA, SSS, or SAS.ASA, AAS, SSA, SSS, or SAS.

42 cm65 cm

82

SAS

Decide whether the following are Decide whether the following are ASA, AAS, SSA, SSS, or SAS.ASA, AAS, SSA, SSS, or SAS.

54

37

32 mm

ASA

Decide whether the following are Decide whether the following are ASA, AAS, SSA, SSS, or SAS.ASA, AAS, SSA, SSS, or SAS.

14

2219 miles

AAS

Decide whether the following are Decide whether the following are ASA, AAS, SSA, SSS, or SAS.ASA, AAS, SSA, SSS, or SAS.

53 yd

87 yd

65

SSA

Law of SinesLaw of Sines

Law of SinesLaw of Sines

a

sin A=

b

sin B=

c

sin C

a

c

bA

B

C

Law of SinesLaw of SinesAASAASASAASASSASSA

28.7102.3

27.4

Solve the following triangle:

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

AAS

Step 1: Determine the Type of Triangle.

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.

ASA82

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…

SummaryIf the triangle is

AASASASSA

If the triangle is

SASSSS

Use the Law of Sines

Coming Tomorrow….. Law of Cosines

Using SASTo findArea!!

One more thing….

Find the area of the triangle:

C = 8430’, a = 16 , and b = 20

C

A

B8430’

16

20

Area = 1/2(side)(side) Sin <

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

Law of CosinesLaw of Cosines

SSSSSSSASSAS

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?

SummaryIf the triangle is

AASASASSA

If the triangle is

SASSSS

Use the Law of Sines

Use the Law of Cosines

Using SSSTo find

Area!!

Theorem Heron’s FormulaThe area A of a triangle with sides a, b, and c is

One more thing…

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

C3B4ME