Use the law of sines to solve the triangle if possible A396

Use the law of sines to solve the triangle, if possible.

A=39.6°, a=23, b=26

According to Law of Sines (a/sinA)=(b/SinB)=(c/sinC)

So, (23/sin39.6) = (26/sinB)

sinB= (26x0.64)/23 = 0.72

so, angle B=sin^-1(0.72) = 46.1⁰

Now in triangle ABC,

we have , angle A+ angleB + angleC=180⁰

So, angle C= 180-39.6-46.1=94.3⁰

Angle C= 94.3⁰

Once again we may use Law of Sines:-

(a/sinA) = (c/sinC)

(23/sin39.6) = (c/sin94.3)

Hence, c = (23x0.997)/0.64 = 35.98

Therefore the triangle is solved as:

A = 39.60, B = 46.10, C = 94.30 and

a = 23, b = 26 and c = 35.98.