Q.162. Properties of triangles.

Question 162.
Solve triangle ABC if A=43.1°, a=186.2 and b=248.6.

Answer 162.
Using sine rule
sinB / b = sinA / a

=> sinB
= (b/a) sinA
= (248.6/186.2) sin(43.1°)
= 65.8°

Also sin(180° - B) = 65.8°
=> B = 114.2° (This is the second solution).

C = 180° - (A + B) = 180° - (43.1° + 65.8°) = 71.1° or
C = 180° - (43.1° + 114.2°) = 22.7°

c = a * (sinC/sinA) = 186.2 * (sin71.1°)/(sin43.1°) = 257.8 or
c = 186.2 * (sin22.7°/sin43.1°) = 105.2.

Answers:
(1) B = 65.8°, C = 71.1°, c = 257.8
(2) B = 114.2°, C = 22.7°, c = 105.2.

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