LC Ordinary Level Solutions Sample Paper 3
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Sample Paper 3: Paper 2
Question 5 (25 marks)
A
Question 5 (a)
2
2
2
Formula: a = b + c − 2bc cos A
c
Question 5 (b) (i)
b
B
C
a
a 2 = b 2 + c 2 − 2bc cos A
30 m
A
BE = 302 + 22.32 − 2(30)(22.3) cos 53o
2
53
B
o
∴ BE = 30 + 22.3 − 2(30)(22.3) cos 53
2
2
o
= 24.3 m
37.5 m
22.3 m
Question 5 (b) (ii)
a 2 = b 2 + c 2 − 2bc cos A
BD = 37.52 + 27.32 − 2(37.5)(27.3) cos 69o
2
∴ BE = 37.5 + 27.3 − 2(37.5)(27.3) cos 69
2
2
69o
E
20 m
= 37.7 m
27.3 m
D
Question 5 (b) (iii)
30 m
A
a 2 = b 2 + c 2 − 2bc cos A
53
2
2(24.3)(37.7) cos B = 24.32 + 37.7 2 − 202
cos B =
24.32 + 37.7 2 − 202
2(24.3)(37.7)
 24.32 + 37.7 2 − 202 
o
B = cos −1 
 = 28.4
 2(24.3)(37.7) 
B
37.7 m
o
69
E
27.3 m
D
Area = 12 ab sin C
Area of lake = Area of ∆ABE + Area of ∆BED + Area of ∆BDC
= 12 (30)(22.3) sin 53o + 12 (24.3)(37.7) sin 28.4o + 12 (27.3)(37.5) sin 69o
= 963 m 2
37.5 m
24.3 m
22.3 m
20 m
Question 5 (b) (iv)
B
o
20 = 24.3 + 37.7 − 2(24.3)(37.7) cos B
2
2
C
o
C