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)/2419π24 and the angle between B and C is (pi)/24π24. What is the area of the triangle?

1 Answer
Ratnaker Mehta
Jul 29, 2016

22 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.

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