1.
Using Sine rule:
sin(A)a=sin(B)b
sin3325=sin47b
b=sin3325×sin47
b=33.57km
Hence, distance of S to B is 33.57km.
sin(B)b=sin(C)c
sin(47)33.57=sin(100)c
c=sin4733.57×sin100
c=45.20km
Hence, the distance of S to A is 45.20km.
2.
To find angle QPR we use the cosine rule:
a2=b2+c2−2bcCosA
CosA=2bcb2+c2−a2
CosA=2×7×872+82−92
CosA=0.2857
A=Cos−1(0.2857)
A≈73.4o
Hence angle QPR is 73.4o
3.
Angle1=3x
Angle2=4x
Angle3=6x
Anglesumpropertyofatriangle=180
3x+6x+4x=180
13x=180
x=13.85
The smallest angle will be: 3x
3x=3×13.85≈41.5o
4.
(a). The angle YZX can be determined by cosine rule:
a2=b2+c2−2bcCosA
CosA=2bcb2+c2−a2
CosA=2×5×952+92−82
A=Cos−1(0.4667)
A≈62.2o
Hence, angle YZX is 62.2o
(b).
To determine the distance Shop X moved to a reach a new location we use the formula:
Distance=360θ×2×π×r
Distance=360o207.8o×2×722×5
Distance≈18.14km
Hence, shop X moved 18.14 km to reach a new location.
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