# Application of the Laws of Sine and Cosine (Math Problem Sample)

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

1. Type out the two equations substituting the numbers from the diagram.

2. Type out the Law of Sines set of relationships and type out the most appropriate version to use the Law of Cosines for this solution.

3. Solve for a using both methods (show step by step work)

Trigonometric Problem

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

1 Type out the two equations substituting the numbers from the diagram.

2 Type out the Law of Sines set of relationships and type out the most appropriate version to use the Law of Cosines for this solution.

3 Solve for a using both methods (show step by step work)

This information can be represented in the figure below.

The sum of the total angles in a triangle = 180

A + B + C = 180

A + 20 + C = 180

A + C = 160

The Sine Rule is given by

aSin A=bSin B=cSin C

Therefore, given b = 30, c = 15, and angle B = 20, we can summarize the rule as

bSin B=cSin C

15Sin 20=30Sin C

15Sine C =30sin20

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