P and Q are respectively the base and the vertex of the tower PQ.AB is another tower which is at a certain distance apart from PQ.The height of AB is less than that of PQ and the base of AB is A.The angles of elevation of Q from A and B are respectively `60^@` and `45^@`.If AB=40m,find PQ,QA and QB.

An observer standing 72 m away from a building notice that the angles of elevation of the top and the bottom of a flag staff on the building are respectively 60^@ and 45^@ .Find the height of the flag staff.

Two poles of equal heights are standing opposite to each other on either side of the road which is 80m wide. From a point between them on the road the angles of elevation of the top of the poles are 60° and 30° respectively. Find the height of the poles .

A line drawn parallel to the base BC of ∆ABC intersects AB and AC at P and Q respectively. If AB = 20 , AC = 15 and AQ = 9 then determine BP.

A line drawn parallel to the base BC of ∆ABC intersects AB and AC at P and Q respectively. If AQ : QC = 7: 4 and AB = 8.8 then determine AP and PB.

A tower makes an angle of 60^@ at a point P lying in the same plane. From a point Q which is at a vertical distance of 10m from P, the angle of depression of the floor of the tower is 30^@ .Find the height of the tower.

A line drawn parallel to the base BC of ∆ABC intersects AB and AC at P and Q respectively. If AB = 12 , AP = 4 , QC = 5 then determine AQ.

The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary.Prove that the height of the tower is 6m.

A TV tower stands vertically on a bank of a canal.From a point on the other bank directly opposite the tower,the angle of elevation of the top of the tower is 60^@ .From another points 20 m away from this point on the line joining this point to the foot of the towre,the angle of elevation of the top of the tower is 30^@ (seeFig).Find the height of the tower and the width of the canal.

A line PQ drawn parallel to the base BC of ∆ABC intersects AB and AC at P and Q respectively. AP = 1/3 PB then determine (area of ABC)/(area of APQ)

AB=h_1 and CD=h_2 are two towers where h_1>h_2 .The angles of depression from the vertex of AB to the vertex and the base of CD are respectively 30^@ and 60^@ .If h_1=60m ,find the distance between the two towers.Also show that h_1-h_2=20m .