Calculate the side lengths a and b to two decimal places.

Answer:Option (a) is correct.a = 15.68 and  b = 19.58Step-by-step explanation:Given: A triangle with some given measurements.We have to find the values of a and b.For a triangle ABC , with side opposite to angle A is a , side opposite to angle B is b and side opposite to angle C is c,Using Sine rule , we have,For the given Δ ABC,∠A = 50° , ∠B = 107°AB = c = 8 , AC = b and BC = aUsing angle sum property of triangle,Sum of angles of a triangle is always 180°So ,  ∠A + ∠B +∠C = 180°Solving for ∠C , we get,∠C = 180° - 107° - 50°∠C = 23°Substitute in Sine rule  , we have,Consider first and last  ratios, we have,Solving for a, we have,We get , a = 15.68Consider last two ratios, we have,and now solving for b ,We get , b = 19.58Thus, option (a) is correct.a = 15.68 and  b = 19.58