Q.171. Properties of triangles.

Question 171.
Given a triangle ABC with a=12, c=21, and B=72degrees, find C.

Answer 171.
Using cosine rule,
cosB = (a^2 + c^2 - b^2) / (2ac)
=> b^2
= a^2 + c^2 - 2accosB
= (12)^2 + (21)^2 - 2*(12)*(21)*cos(72°)
= 144 + 441 - 155.7
= 429.3
=> b = 20.72

Using sine rule,
sinC / c = sinB / b
=> sinC = (c/b) sinB
=> sinC = (21/20.72) sin(72°)
=> C = 74.6°.

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