Question

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?

Answer 1

`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.