Answer: BM = 21.4
Step-by-step explanation:
Considering the given triangle BMS, to determine angle BM, we would apply the sine rule. It is expressed as
m/SinM = s/SinS = b/SinB
Where m, s and b are the length of each side of the triangle and angle M, Angle S and angle B are the corresponding angles of the triangle.
From the information given,
Angle M = 102°
Angle B = 35°
Angle S = 180 - (102 + 35) = 43°
b = MS = 18
s = BM
Therefore
18/Sin 35 = BM/Sin 43
Cross multiplying, it becomes
BMSin35 = 18 × Sin 43
BM × 0.5736 = 18 × 0.6820
0.5736BM = 12.276
Dividing the left hand side and the right hand side of the equation by 0.5736, it becomes
0.5736BM/0.5736 = 12.276/0.5736
BM = 21.4
