For a triangle abc, find the measure of segment ab given m∠a = 55°, m∠b = 44°, and b = 68.

Using SINE LAW or Rule of SINE For triangles, states that given 2 angles and 1 side, one can compute for using below equation

 

a/sinA = b/sinB = c/sinC, Where a & A are opposite to each other.

 

Thus we have segment AB which is equal to side C, manipulating the equation we have

Given : angle a = 55, angle b = 44, Therefore angle c = 180 – (55+44) = 81 deg

(AB or Side opposite of Angle C)/sin(81 deg) = b (or segment CA/AC )/sin(44 deg)

AB = sin(81 deg) * (b = 68 / sin (44 deg))

AB = 96.68, see attached image as guide

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