Let B = 5.50 m at 60º. Let C have the same magnitude as A and a direction angle greater than that of A by 25º. Let A•B = 27.6 m^2 and B•C = 33.9 m^2. Find the magnitude and direction of A.

Question

Let B = 5.50 m at 60º.  Let C have the same magnitude as A and a direction angle greater than that of A by 25º.  Let A•B = 27.6 m^2 and B•C = 33.9 m^2.  Find the magnitude and direction of A.

anonymous · Answer

so i am considering the horizontal as the refrence.. 

lets say A makes an angle theta with the horizontal.. 

then the angle made by A with B is theta - 60 (or 60 - theta. doesn't matter)

A.B= 27.6 there fore$$ABcos( \theta - 60) = 27.6 ----------(1)$$

C has the same mangnitude as A and makes angle with horizontal 25 + theta

B.C= 33.9.. so similary build the second equation ..
since B value is known to you.. you ll have two equations in 2 variables (A and theta).. solve it