A rod of steel is fixed at A(4,0) and a toy is placed on it at B(0,4). Now rod is rotated about A through an angle of 15degree in clockwise direction, then find the new position of a toy.

Length of Rod: Using Pythagoras theorm, P^2+b^2=H^2 ==> p^2= 4^2+4^2=32 ==> p=4*root(2)

When the rod is rotated by an angle of 15, then a^2+(a*root(3))^2 ==> 4*a^2 =32 ==> a=2*root(2)

Similarly a*root(3)= 2*root(6)

x= 4-(2*root(2))

y= 2*root(6)

The new coordinates will be (4-(2*root(2)),2*root(6))