Question

In the triangle ABC AB=12cm angle BAC=60 and ACB is 45 find the exact length of BC?

Answer 1

BC = `6sqrt(6)`

Explanation:

Angle `ABC = 180^o-(60^o +45^o)=75^o`

Using The Sine Rule:

`sinA/a=sinB/b=sinC/c`

`sin(60^o)/a=sin(45^o)/12=>a=(12sin(60^o))/sin(45^o)=((12sqrt(3))/2)/(sqrt(2)/2)=(12sqrt(3))/sqrt(2)=(12sqrt(6))/2=6sqrt(6)`