Answer:
Step-by-step explanation:
The diagram of the triangles are shown in the attached photo.
1) Looking at ∆AOL, to determine AL, we would apply the sine rule
a/SinA = b/SinB = c/SinC
21/Sin25 = AL/Sin 105
21Sin105 = ALSin25
21 × 0.9659 = 0.4226AL
AL = 20.2839/0.4226
AL = 50
Looking at ∆KAL,
AL/Sin55 = KL/Sin100
50/0.8192 = KL/0.9848
50 × 0.9848 = KL × 0.8192
KL = 49.24/0.8192
KL = 60
AK/Sin25 = AL/Sin 55
AKSin55 = ALSin25
AK × 0.8192 = 0.4226 × 50
AK = 21.13/0.8192
AK = 25.8
2) looking at ∆AOC,
Sin 18 = AD/AC = 18/AC
AC = 18/Sin18 = 18/0.3090
AC = 58.25
Sin 85 = AD/AB = 18/AB
AB = 18/Sin85 = 18/0.9962
AB = 18.1
To determine BC, we would apply Sine rule.
BC/Sin77 = 58.25/Sin85
BCSin85 = 58.25Sin77
BC = 58.25Sin77/Sin85
BC = 58.25 × 0.9744/0.9962
BC = 56.98
