Question

A triangle has sides A, B, and C. The angle between sides A and B is `(5pi)/6` and the angle between sides B and C is `pi/12`. If side B has a length of 7, what is the area of the triangle?

Answer 1

The Area is `12.25` square units

Explanation:

The angle between sides A and B `/_C= 5*180/6=150^0`
The angle between sides B and C `/_A= 180/12=15^0`
The angle between sides C and A `/_B= 180-(150+15)=15^0`
By sine law , we know `A/sinA=B/sinB=C/sinC :. A=SinA/sinB*B=7*sin15/sin15=7` Now `A=7 ; B=7` and their included angle `/_C=150^0 :.`The Area `=A*B*sinC/2=7*7*sin150/2 =12.25` square units[Ans}