A statue 1.46 m tall stand on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60^o and from the same point, the angle of elevation of the top of the pedestal is 45^o . Find the height of the pedestal. \((\sqrt { 3 } =1.73)\) .

On a horizontal plane there is a vertical tower with a flag pole on the top of the tower. At a point 9 metres away from the foot of the tower the angles of elevation of the top and bottom of the flag pole are 60^o and 30^o respectively. Find the heights of the tower and flag pole mounted on it.

A ladder of length 6 m makes an angle of 45^o with the floor while leaning against one wall of a room. If the foot of the ladder is kept fixed on the floor and it is made to lean against the opposite wall of the room, it makes an angle of 60^o with the floor. Find the distance between these two walls of the room.

The horizontal distance between two poles is 15 m. The angle of depression of the top of first pole as seen from the top of second pole is 30^o . If the height of the second pole is 24 m, find the height of the first pole. \((Use\sqrt { 3 } =1.732)\)

The length of the shadow of a tower standing on level ground is found to 2 x metre longer when the sun's altitude is 30^o than when it was 45^o. Prove that the height of tower is \(x(\sqrt { 3 } +1)\) metres.

Two boats approach a lighthouse in mid - sea from opposite directions. The angles of elevations of the top of the lighthouse from two boats are 30^o and 45^o respectively. If the distance between two boats is 100 m, find the height of the lighthouse.

A man who is \(1\frac { 3 }{ 4 } \)tall sees that angle of elevation

From the top of a hill \(200\sqrt { 3 } \) m high, the angle of depression of a ship moving towards the hill is 30°. After 2 min, its angle of depression becomes 60°. Find the speed of the ship assuming it to be uniform.

There is a small island in the middle of a 100m wide river and a tall tree stands on the island. P and Q are points directly opposite to each other on two banks and in line with the tree. If the angles of elevation of the top of the tree from p and Q are respectively \({ 30 }^{ \circ }\)and \({ 45 }^{ \circ }\)
(i) Find the height of the tree. [take, \(\sqrt3\) = 1732]
(ii) Determine the distance between two trees.
(iii) Which point is farthest from the island?

From a 60 m high building, the angle of depression of the top and bottom of a lamppost are \({ 30 }^{ ° }\)and \({ 60 }^{ ° }\) , respectively. Find the distance between lamppost and building. Also, find the difference of heights between building and lamppost.

If 300\(\sqrt { 3 } \) m high tower makes angle of elevation at a point on ground which is 300 m away from its foot, then find the angle of elevation.

A bridge on a river makes an angle of 45\(°\) with its edge. If the length along the bridge from one edge to the other is 150 m, then find the width of the river.

A straight tree is broken due to thunderstorm. The broken part is bent in such a way that the peak of the tree touches the ground at an angle of 60\(°\)at a distance of \(2\sqrt { 3 } m\) Find the whole height of the tree.

Determine the height of a mountain, if the elevation of its top at an unknown distance from the base is 30\(°\)  and at a distance 10 km further off from the mountain, along the same line, the angle of elevation is 15\(°\) (Take tan 15\(°\) = 0.27) 

There is a flag staff on a tower of height 20 m. At a point on the ground, the angles of elevation of the foot and top of the ground, the angles of elevation of the foot and top of the flag are 45\(°\) and 60\(°\) respectively. Find the height of the flag staff.