Question

The height of a tower is 50 m. When the sun’s altitude changes from 30° to 45°, the shadow of the tower becomes “ x ” metres less. Find the value of “ x ” .



A 1.6 m tall girl stands at a distance of 3.2 m from a lamp post and casts a shadow of 4.8 m on the ground. Find the height of the lamp post by using trigonometric ratios.



The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of top of the tower from the foot of the hill is 30°. If the tower is 50 m high, what is the height of the hill?



The shadow of a tower standing on level ground is found to be 45 m longer when Sun’s altitude is 30°, than when it was 60°. Find the height of the tower.



A tree breaks due to a storm and the broken part bends so that the top of the tree touches ground making an angle of 30° with the ground. The distance from the foot of the tree to the point where the top touches the ground, is 10 metres. Find the height of the tree.



As observed from the top of a light house, 100 m above sea level. The angle of depression of a ship sailing directly towards it, changes from 30° to 45°. Determine the distance travelled by the ship during the period of observation.



The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60°. At a point Y, 40 m vertically above X, the angle of elevation is 45°. Find the height of the tower PQ and the distance XQ.



The horizontal distance between two towers is 140 m. The angle of elevation of the top of the first tower when seen from the top of the second tower is 60 m, find the height of the first tower.



An aeroplane flying horizontally 1 km above the ground is observed at an elevation of 60°. After 10 seconds, its elevation is observed to be 30°. Find the speed of the aeroplane in km/hr.



The angle of elevation of the top of a tower from two points on the ground at distances a meters and b meters from the base of the tower and in the same straight line are complementary. Prove that the height of the tower is metres.



A pole 5 m high is fixed on top of a tower. The angle of elevation of the top of the pole observed from a point A on the ground is 60° and the angle of depression of point A from the top of the tower is 45°. Find the height of the tower. (take = 1.732)



A window in a building is at a height of 10 m from the ground. The angle of depression of a point P on the ground from the window is 30°. The angle of elevation of the top of the building from the point P is 60°. Find the height of the building.



From a building 60 metres high, the angles of depression of the top and bottom of lamppost are 30° and 60° respectively. Find the distance between the lamppost and building. Also find the difference of heights between building and lamppost.



Two pillars of equal height stand on either side of a roadway which is 150 m wide. From a point on the roadway between the pillars, the elevations of the top of the pillars are 60° and 30°. Find the height of the pillars and the position of the point.



A man standing on the deck of a ship which is 10 m above water level, observes the angle of depression of the base of the hill as 60° and angle of depression of the base of the hill as 30°. Find the distance of the hill from the ship and height of the hill.

Answer 1

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Answer 2

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