Policemen, Mr Peter and Mr Roger, are doing a search-and-rescue operation at Sunshine Town yesterday. The team of policemen has to search a triangular area PQR for Mrs Queen’s baby. Mr Peter is stationed at point P and Mr Roger is stationed at point R. Point Q is where Mrs Queen’s house is located.


Mr Peter is 32 km away from Mrs Queen’s house and 40 km away from Mr Roger. Mrs Queen’s house is southwest of Mr Peter and the bearing of Mr Roger from Mr Peter is 120o.
(a) Calculate the area PQR which the policemen have to search.
(b) Find the distance between Mr Roger and Mrs Queen’s house.


Suddenly, Mr Peter heard a cry and spotted Mrs Queen’s baby in a bush at point B inside the triangular area PQR. The bearings of the baby from Mr Peter and Mr Roger are 174o and 065o respectively.
(c) Calculate how far away Mr Peter is from the baby so that he can be there as soon as possible.
(Hint: Draw a diagram before attempting to solve the problem.)

luv,
ms ang