The law of sines relates the interior angles of a triangle to the lengths of the

Question

The law of sines relates the interior angles of a triangle to the lengths of the opposite sides. Mathematically for a triangle with interior angles a, b, and c with opposite sides A, B, and C, (see figure below) we can express the law of sines as follows. A/sin(a) = B/sin(b) = C/sin(c) Consider a triangle for which the length of side A = 197 mm, the length of side B = 1.90 in, and the angle a = pi/3 radians. Determine the length of side C in inches and the angles b and c in degrees. In your solutions take the angle b as acute. c = _____ in b = _____ degree c = _____ degree

Explanation / Answer

Sine law,

A / sin(a) = B / sin(b)

197 / sin(pi/3) = (1.90 x 25.4) / sin(b)

sin(b) = 0.122

b = 12 deg .........Ans

a + b + c = 180 deg

(pi / 3 rad) + (12 deg ) + c = 180

60 + 12 + c = 180

c = 108 deg ........Ans

B / sin(b) = C / sin(c)

1.90 / sin(12.2) = C / sin(107.8)

C = 8.6 inch ..........Ans

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