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# Sine and Cosine Rule

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by

## Mr Mattock

on 30 January 2018

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#### Transcript of Sine and Cosine Rule

Sine and Cosine Rule
Example
Example
Solving triangle problems
Use sine and cosine rule to solve problems in non-right triangles.
9 cm
12 cm
63
o
A
B
C
Find the angle ABC.
Starter
9 cm
12 cm
63
o
A
B
C
Find the angle ABC.
BC = 9 + 12 - 2(9)(12)Cos63
BC = 81 + 144 - 216Cos63
BC = 126.9380521
BC = 126.9380521 = 11.3 cm
2
2
2
2
2
Sin ABC 9
Sin 63 11.266...
=
9
11.266...
Sin ABC = x Sin 63
Sin ABC = 0.711750004
ABC = Sin 0.71175004 = 45.4
-1
o
15 cm
6 cm
98
o
A
B
C
Find the length BC.
Solving triangle problems
15 cm
6 cm
98
o
A
B
C
Find the length BC.
Sin BCA 6
Sin 98 15
=
Sin BCA = 0.4 x Sin 98
Sin BCA = 0.396107227
BCA = Sin 0.396107227 = 23.33504691
-1
o
So angle BAC = 180 - 98 - 23.335... = 58.66495309
o
BC Sin 58.66495309
15 Sin 98
=
BC = x 15
Sin 58.66495309
Sin 98
BC = 12.9 cm
A car travels 17 km from point A on a bearing of 040 to point B. The car then travels 25 km on a bearing of 072 to point C. Find the bearing and distance of C from A.
o
o
Example
A car travels 17 km from point A on a bearing of 040 to point B. The car then travels 25 km on a bearing of 072 to point C. Find the bearing and distance of C from A.
o
o
140
148
AC = 17 + 25 - 2(17)(25)Cos148
AC = 1634.840882
AC = 1634.840882 = 40.4 km
Sin BAC 25
Sin 148 40.433...
=
Sin BAC = x Sin 148

Sin BAC = 0.327651357

BAC = Sin 0.327651357 = 19.1
Bearing = 40 + 19.1 = 59.1
25
40.433...
2
2
2
2
o
o
Activity
Complete the worksheet about the Sine and Cosine rule.
Activity
Activities
Activity

Key
Examples

Worked
Example

Worked
Example

Worked
Example

Starter
Full transcript