# 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

Trigonometric Function

Solving a Triangle

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Date

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

aSin A=bSin B=cSin C

15Sin 20=30Sin 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

a2=b2+c2

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