Warm Up 4/201. Find the area: Round to the nearest meter.

33m

39m

61A

B

C

2. Find the missing angle measure: Round to the nearest tenth.

34ft

48ft

44

x

3. Find the missing side length: Round to the nearest tenth.

40cm n

59 46

563m2 78.70

47.7 cm

12.4 Law of Cosines – part 1

If you do not have a right triangle you use Law of Sines or Law of cosines.SOH CAH TOA only works in right triangles

Law of cosine: c2 = a2+b2 – 2abcos C Other two sides

Opposite side and angle

A B

C

c

ab

Law of cosines: c2 = a2+b2 – 2abcos C

Finding a Missing Side Length

36o

45 m

52 m

x

Step 1: Identify the opposite side/angleStep 2: Plug into law of cosines formulaStep 3: Solve using your calcStep 4: Last step is to take the square root

To use law of cosines to find a side you must have SAS

Example 1: Find the length of x Step 1: identify the opposite side/angle

Step 2: plug into law of cosines formula Step 3: solve using your calc Step 4: last step is to take the square root

)36cos(524525245 222 x

36o

45

52

x80.9422 x

7.30x

Example 2:

22

)70cos(312223122 222 x

70o

31

3.31

48.9782

x

x

I must see this step on your homework for credit

x

Example 3: Two 11-cm radii of a circle form a central

angle measuring 115o. What is the length of the chord connecting the two radii?

Draw and label a picture

11

11115

x2 = 112 +112 – 2(11)(11)cos(115)

x2= 344.27

X = 18.6 cm

Law of cosine: c2 = a2+b2 – 2abcos C

Finding Missing Angle Measures

Q E225

250175

D

Example 1: Find QD

2 2 2250 175 225 2 175 225 cosQ

Q E225

250175

Start with the side across from the angle you are looking for

You must solve in steps

62500 81250 78750 cosQ -81250-81250

18750 78750 cosQ -78750 -78750

.2381=cosQ

Q = 76.2o

Last step is inverse (you are looking for an angle)

Use cos(.2381)

CLT

Undo +/-

Undo ×/÷

Find all missing angles- round to the nearest degree

512 2 270 62 51 2 62 51 cos A

70

62A

C

B

1. Find the largest angle first (remember, the largest angle is across from the largest side)

4900 6445 6324 cos A 1545 6324 cos A

.2443 cos

76

A

A

2. Find the smallest using law of sines

51

sin

70

76sin B

76o

45B 3. Find the last angle by subtracting

the other two from 180

C =180 – (76+45)= 59°

Given only the sides use Law of Cosines to find an angle…This is a special case when solving for an angle. Start with the largest side then find the smallest angle.

Next, find the smallest angle

45°

59°

CLT

Undo +/-

Undo ×/÷

Use cos(.2443)

Cross multiply!!

Example 3: The diagonals of a parallelogram are 60 in and 70in and

intersect at an angle measuring 64o. Find the length of the shorter side of the parallelogram. Round to the nearest tenth place.

Draw a picture

60

70

64o x30

35

2 2 2

2

30 35 2 30 35 cos 64

1204.42

34.7

x

x

x

Homework:

WS: 12.4

Summary:

What information do you need to use Law of Cosines?