# Understanding the Law of Sines and Cosines (Math Problem Sample)

the mathematics problem required knowledge on the law of sines and cosines. to solve the problem i first drew a triangle for clear demonstration of the question at hand. t

the triangle was labelled abc. the measurements given in the question were then filled in the triangle.

THEN THE LAW OF SINES AND COSINES IS DEFINED.

then we used the law of sines and cosines to find angle a, as required by the question.

Question 1Solve for α in the oblique triangle ABC; AB = 30; AC = 15 and angle B = 20°

Oblique triangle ABC; AB = 30; AC = 15 and angle B = 20°

1 Type out the two equations substituting the numbers from the diagram.DemonstrationDrawing out the triangle first:

10096502971800A

c= 30 b=15 B a Cangle ABC=20° (β)angle ACB=Ɣangle BAC=α ( This is the angle in question) Solution

Equation 1 (obtained from the law of cosines)

b2=a2+c2-2ac(cos b)(We are going to choose this equation because we only have one unknown. That is, a.) Substituting the values from the diagram above, where: b = 15 c =30

β = 20°)Therefore Equation 1 is;

152=a2+302-2a.30.(cos20°)

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