双语教学课件：Sine and cosine
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A B
1.５m
┛ ┓
36
C
D
7.2m
Brief summary: 1、Use the sine rule if you know two sides and the angle opposite one side or you know two angles and a side. 2、Use the cosine rule if you cannot use the sine rule. 3、When you use the sine rule to find an angle, you should think if the angle is obtuse(钝角）.
2 2 2
b c a cos A 2bc
2 2
2
a b c cosC 2ab
2 2
2
a c b cos B 2ac
2 2
2
Question1: Q is 25 km from P on a bearing（方位角） of 75 and 40 km from R ．P is due North（正北方） of R. Calculate the bearing of Q from R. N
Sine and Cosine Rules 正弦(余弦)定理 (二)
制作人：桐乡市高级中学 刘爱纯
Review:
1. Sine Rule
a b c sin A sin B sin C
2R
2、Cosine Rule
a b c 2bc cos A
2 2 2
Βιβλιοθήκη Baidu
b a c 2bc cos B 2 2 2 c a b 2ab cosC
B
Question4: The diagram(图) shows the cross-section( 横截面 ) of a roof( 屋顶 ). Calculate angles x, y and z.
x y
B
A
z
11.5m
C
Question5: calculate the length of the ramp(斜坡), BC.
75
P
R
Q
Question2: Find the length BC and the angle B. B
30
C
A
Question3: Find the length BC and the angle B. B
30
A 22mm
C
C
b A
C
a
B
b
A B 2
a
a
B1
a
b A
a B
C
b
A
THANKS！
1.５m
┛ ┓
36
C
D
7.2m
Brief summary: 1、Use the sine rule if you know two sides and the angle opposite one side or you know two angles and a side. 2、Use the cosine rule if you cannot use the sine rule. 3、When you use the sine rule to find an angle, you should think if the angle is obtuse(钝角）.
2 2 2
b c a cos A 2bc
2 2
2
a b c cosC 2ab
2 2
2
a c b cos B 2ac
2 2
2
Question1: Q is 25 km from P on a bearing（方位角） of 75 and 40 km from R ．P is due North（正北方） of R. Calculate the bearing of Q from R. N
Sine and Cosine Rules 正弦(余弦)定理 (二)
制作人：桐乡市高级中学 刘爱纯
Review:
1. Sine Rule
a b c sin A sin B sin C
2R
2、Cosine Rule
a b c 2bc cos A
2 2 2
Βιβλιοθήκη Baidu
b a c 2bc cos B 2 2 2 c a b 2ab cosC
B
Question4: The diagram(图) shows the cross-section( 横截面 ) of a roof( 屋顶 ). Calculate angles x, y and z.
x y
B
A
z
11.5m
C
Question5: calculate the length of the ramp(斜坡), BC.
75
P
R
Q
Question2: Find the length BC and the angle B. B
30
C
A
Question3: Find the length BC and the angle B. B
30
A 22mm
C
C
b A
C
a
B
b
A B 2
a
a
B1
a
b A
a B
C
b
A
THANKS！