April 4April 4thth

copyright2009merrydavidsoncopyright2009merrydavidson

April 4April 4thth

copyright2009merrydavidsoncopyright2009merrydavidson

CALCULATOR TODAY

Happy Summer Birthdays to:

Timmy Manley: 7/5th

Andrew Krasner: 8/14th

OBLIQUE TRIANGLES6.1 & 6.2

A triangle with NO right angles.

ANGLES/CAPITAL LETTERS

sides/small letters

A

B Ca

bclittle a is across from Big A

put calculator in

degree mode

SOLVE the triangleMeans to find the length of all sides and the measure of all angles.

To solve oblique triangles two pieces of information are needed and a TRIG FUNCTION.

Round sides to the nearest TENTH and angles to the nearest DEGREEunless otherwise

noted.

LAW OF SINES (you will use 2 of the 3 sections to make a proportion.

C

c

B

b

A

a

sinsinsin

Memorize this……..

This formula states that the ratio of any side of a triangle to the sine of the angle opposite that side is a constant (proportional) for a given triangle.

EX 1: Given triangle ABC with the measures shown below,

find b?

8

sin 57 sin 74

b57O 49O

AB

C

8

START with a chart.

Fill in what you know

Find angle C.

Solve the proportion

74

bsin74 = 8sin57

b = 8sin57 sin74

approx 7.0

a= b= c=

A= B= C=

a= b= c=8

A= 49 B=57 C=

EX 2: In triangle ABC if

A = 32, B = 57, and c = 14. Find angle C and

sides a and b.

a = b = c =

A = B = C =

7.4

11.7

91

a

b

C

You do this one. In a minute I will show you the answer.

EX 3: In triangle ABC, A = 1100, b = 7 and a =

9. Find angle B.a = b = c =

A = B = C =

47B

9 7

sin110 sin B

7sin110 = 9sinB

sinB = 7sin110 9

Use sine inverse1 7sin110

sin ( )9

B

EX 4: Given an oblique triangle with angle A = 490, and side

a = 8 and side b = 9, find angle B.

a = b = c =

A = B = C =

58B

You do this one. In a minute I will show you the answer.

EX 5: Find b

a = 10 b = c = 7

A = B = 51 C =

B C10

7 b

51O

A

a = b = c =

A = B = C =

You can not make a proportion

LAW OF COSINES is used when you can

not make a proportion.

6.2

a2 = b2 + c2 – 2bc cos A

b2 = a2 + c2 –2ac cos B

c2 = a2 + b2 – 2ab cos C

Memorize these……..

EX 5: Find b

B C10

7 b

51O

Aa = 10 b = c = 7

A = B = 51 C =

Using the law of cosines…..

b2 = a2 + c2 -2ac cos B

b2 = 102 + 72 -2(10)(7) cos 51

60.9b

EX 6: SOLVE the triangle.

A B7

5 4

C

a = 4 b = 5 c = 7

A = B = C =

Always find the “biggest” angle first! So find C.

“store” this to find the other parts.

c2 = a2 + b2 -2ab cos C72 = 42 + 52 -2(4)(4) cos

C49 = 41-2(4)(4) cos C

8 = -2(4)(4) cos C

1 8cos ( ) 104

32C

EX 6: SOLVE the triangle.

A B7

5 4

C

a = 4 b = 5 c = 7

A = B = C = 104

Now use Law of Sines

to find A or B. Then

use the sum of angles in

a triangle is 180o to

find the other angle.

44

32

B

A

EX 7: SOLVE the triangle.

B C6

8 b

60O

A

a = b = c =

A = B = C =

What should you find first???

little b

7.2bStore this!

Now find angle A or C.

46

74

A

C

EX 8: Find cos X; given x = 5, y = 3 and z = 6 in triangle XYZ.

x = y = z =

X = Y = Z =

5cos

9X

HW: WSand work on TAKS packet

for additional help on law of sines and/or cosines,

go to the internet or come in to see me.