Solve the following triangle completely. (a). in triangle ABC, B = 25.6° C = 124.4° C= 39.2m
(b) B = 101.15°, b= 17.23cm and C= 10.86cm.

The answers is below in bold.

Step-by-step explanation:

(a) A = 180 - 25.6 - 124.4 = 30 degrees.

Next use the Sine Rule:

b / sin B = c / sin C

b / sin 25.6 = 39.2/sin 124.4

b = (39.2 * sin 25.6) / sin 124.4

b = 20.53 m.

Also

a / sin A = c / sin C

a / sin 30 = 39.2 / sin 124.4

a =  (39.2 * sin 30 / sin 124.4

a = 23.75 m.

b). This is solved in a similar way to (a).

First find angle C  using the sine rule.

Then you will know angle A  from the 180 degree Rule.

Then you can find the length of  a using the Sine Rule.

i think it is x = 1.2

a² + b²= c²

24² + 7² = c²

c= 25