Question

Solve the triangle if c = 10 and A = 50 degrees

Answer 1

Answer:

Step-by-step explanation:

Since A = 50 degrees, c = 10 ,and since it is a right Triangle, then C = 90 degrees and so B = 180 - (90 +50)......... sum of angles of a triangle

                            B = 180 - 140

                             B = 40 degrees

Using sine rule : a/sin A = b / sin B = c / sin C

To calculate a, then we use a/ sin A = c / sin C , since we know c and C

i.e a/ sin 50 = 10 / sin 90

recall that sin 90  = 1

then we have a / sin 50 = 10 / 1

cross multiply

a = 10 x sin 50

 a = 10 x 0.76604

  a = 7.6604

We will calculate b following the same procedure

b/ sin B = c / sin C

b/ sin 40 = 10/ sin 90

b/ sin 40 = 10/ 1

           b = 10 x sin 40

            b = 10 x 0.64279

             b = 6.4279

Therefore a ≈7.6604  , b ≈ 6.4279