A farmer owns a triangular field ABC. One side of the triangle, AC, is 104 m, a second side, AB, is 65 m and the angle between the two sides is 60 degrees.
(a) Given that sin60 = √3/2, find the area of the field in the form p√3 wehre p is an integer.
Let D be a point on BC such that AD bisects the 60 degree angle. The farmer divides the field into two parts A1 and A2 by constructing a straight fence AD of length x meters.
(b) (i) show that the area of A1 is given by 65x/4.
(ii) Find a similar expression for the area of A2.
(iii) hence, find the value of x in the form q√3, where q is an integer.
(c) (i) explain why sinA(angle D)C = sinA(angle D)B.
(ii) use the result of part (i) and the sine rule to show that BD/DC = 5/8