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Elementary Mathematics || Trigonometry || Heights & Distances

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Question 1

From two points on the ground lying on a straight line through the foot of a pillar, the two angles of elevation of the top of the pillar are complementary to each other. If the distance of the two points from the foot of the pillar are 9 metres and 16 metres and the two points lie on tye same side of the pillar, then the height of the pillar is

Question 2

At an instant, the length of the shadow of a pole is times the height of the pole. The angle of elevation of the Sun at that moment is

Question 3

An aeroplane when flying at a height of 5000m from the ground passes vertically above another aero plane at an instant, when the angles of elevation of the two aero planes from the same point on the ground are 60 °and 45 ° respectively. The vertical distance between the aero planes at that instant is:

Question 4

There is a small island in the middle of a 100m wide river, There is a tall tree on the island. Points P and Q are points directly opposite to each other on the two banks and in line with the tree. If the angles of elevation of the top of the tree at P and Q are 30° and 45°, then the height of tree is:

Question 5

Two poles of height 7 m and 12 m stand on a plane ground. If the distance between their feet is 12 m then the distance between their top will be how much?
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Aug 24CDS & Defence