Question

Given that A=84, B=66 and a=13 solve triangle ABC. Round to the nearest hundredth.

Answer 1

In this item, we are asked to determine the sides and the angles of the given triangle ABC. We use the cosine law for the first one,

                           A/cos A = B/cos B

Substituting,
                       84 / cos 13° = 66/ cos b
The value of b is equal to 40°.

The sum of the measures of the angle in the triangle is equal to 180°
                               a + b + c = 180°
          
                              13 + 40 + c = 180°
     
                                     c = 127°

Use again Sine Law,
                           B/ sinb= C / sin c

Substituting,
                           66/sin 13 = C/sin  .
The value of c from the equation is  127.32.