A triangle has sides A, B, and C. Sides A and B have lengths of 8 and 1, respectively. The angle between A and C is #(19pi)/24# and the angle between B and C is # (pi)/24#. What is the area of the triangle?

1 Answer
Jul 29, 2016

#2# sq.unit.

Explanation:

We know that the area of a #Delta# with sides A,B,C can be found by using any one of the following formulas :

Area#=1/2BCsin(hat(B,C))=1/2CAsin(hat(C,A))=1/2ABsin(hat(A,B))#,

where, #hat(A,B)# denotes the angle btwn. sides #A and B#, & likewise.

We are given the lengths of sides #A=8 and B=1#, hence, the last formula will be more useful. Yes, that will require #hat(A,B)#, which can be easily obtained by,

#hat(A,B)=pi-hat(B,C)-hat(C,A)=pi-(pi/24+19pi/24)=4pi/24=pi/6#

Therefore, Area of the #Delta=1/2*8*1*sin(pi/6)=4*1/2=2# sq.unit.