Trigonometry Problem (Math Problem Sample)

Solve for α in the oblique triangle ABC; AB = 30; AC = 15 and angle B = 20°
Solve for α in the oblique triangle ABC; AB = 30; AC = 15 and angle B = 20°

Given: b = 15, c = 30 and ∠ B = 20°
A + B + C = 180
A + 20 + C = 180
A + C = 160
From Sine rule
a/(Sin A)=b/(Sin B)=c/(Sin C)
15/(Sin 20)=30/(Sin C)
Sin C=2Sin 20
Sin C = 2Sin 30
= 0.6840
C = Sin-1 0.6840
= 43.16
A + C = 160
A = 160 – 43.16
= 116.84
From Cosine rule
a^2=b^2+c^2-2bcCosA
a^2=30^2+15^2-2x30x15Cos116.84
a^2=1125-(-406.35)
a^2=1531.35
a=39.13
Verifying the value of a using the sine rule
a/(Sin A)=b/(Sin B)
a/(Sin 116.84)=15/(Sin 20)
a=(15 ×Sin116.84)/(Sin 20)
a=39.13