A scalene triangle ABC has side lengths AB=6cm, BC=4cm, and AC=x cm. The angle A, opposite BC, is 40 degrees and the angle B, opposite AC, is 50 degrees. State the sine rule and use it to find the value of x to 3 s.f.

The sine rule states that for any scalene triangle ABC the following equation holds: BC/sin(A) = AC/sin(B) = AB/sin(C).[Draw a diagram.] By drawing the triangle and substituting the values that we know into the equation, we get the following: 4/sin(40) = x/sin(50) = 6/sin(C)Angle C does not help us find x so we focus on the left-hand equation: 4/sin(40) = x/sin(50) Then multiply through by sin(50) to make x the subject and get: x = 4*sin(50)/sin(40) Use your calculator to obtain the value of x: x = 4.76701437 The question has asked us for an answer to 3 significant figures though, so we round to x = 4.77.