EXTRA QUESTIONS CLASS X CH-9 APPLICATIONS OF TRIGONOMETRY

2 marks questions

Q.1) If a tower is 30m high ,casts a shadow 10√3 m long on the ground,then what is the angle of elevation of the sun?

Q.2) If the angle of elevation of the tower from a distance of 100m from its foot is 60° ,then what will be the height of the tower?

Q.3) If a pole 12m high casts a shadow of 4√3 m long on the ground,find the sun's elevation.

Q.4) An observer 1.7m tall is 20√3m away from the tower. The angle of elevation from the eye of observer to the top of tower is 30° . Find the height of tower.

Q.5) A ladder leaning against the wall, makes an angle 60° with the horizontal. If the foot of the ladder is 2.5m away from the wall, find the length of the ladder.

Q.6) The angle of elevation of the top of a tower from a point on the ground, which is 30m away from the foot of the tower is 30° . Find the height of the tower.

Q.7) The ratio of the height of a tower and the length of its shadow on the ground is √3:1. What is the angle of elevation of the sun?

Q.8) A circus artist is climbing a 20m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle of elevation is 30°. 

Q.9) The height of a tower is 12m . What is the length of its shadow when sun's altitude is 45°?

Q.10) The angle of elevation of the top of a tower from a point on the ground, which is 30m away from the foot of the tower is 30°. Find the height of the tower.

3 marks questions

Q.1) On a straight line passing through the foot of a tower, two points C and D are at the distances of 4m and 16m from the foot respectively. If the angles of elevation from C and D of the top of the tower are complementary and angle of elevation at C is 60° then find the height of the tower.

Q.2) Two men on either side of a 75m high building and in line with base of building observe the angle of elevation of the top of the building as 30° and 60°. Find the distance between the two men. (Use √3=1.73)

Q.3) As observed from the top of a 75m high lighthouse from the sea level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

Q.4) A contractor plan to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5m , and is inclined at an angle of 30° to the ground, whereas for elder children,she wants to have a steep slide at the height of 3m , and inclined at an angle of 60° to the ground. What should be the length of the slide in each case?

Q.5) A kite is flying at a height of 60m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60° . Find the length of the string, assuming that there is no stack in the string.

Q.6) A tree breaks due to storm and the broken part bends , so that the top of the tree touches the ground making an angle of 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8m . Find the height of the tree.

Q.7) 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 10km further off from the mountain, along the same line, the angle of elevation is 15° . (Use tan 15°=0.27)

Q.8) From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45° respectively. If the bridge is at a height of 3m from the banks , find the width of the river.

Q.9) A TV tower stands vertically