Question

In triangle abc angle a = 40◦, side b = 11 and side c = 5. use the cosine rule to find the length of side a, to two decimal places. without using the cosine rule again, find the remaining angles b and c, giving your answers to the nearest degree.

Answer 1

A^2 = b^2 + c^2 - 2bc cos a

    = 11^2 + 5^2 - 2*5*11 cos 40

   =  7.86 to 2 DP's

to find the remaining angles use the sine rule:-
a / sin A = b / sin B so

7.857/ sin 40 =  11 / sin B
sin B = 11 sin40 / 7.857 = 0.8999

<B = 64 degrees 

so <C = 180 - 64-40  =  76 degrees