test paper of class 10th

3E coaching classes

class10th  chapter  some application of trigonometry

1.The angle of elevation of the top of a building from the foot of the tower is 30° and the angle
  of elevation of the top of the tower from the foot of the building is 60°. If the tower is 60 m high,
  find the height of the building.

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

3.A boy standing on a horizontal plane finds a bird flying at a distance of 100 m from him at an
  elevation of 30°. A girl standing on the roof of 20 metre high building, finds the angle of
   elevation of the same bird to be 45°. Both the boy and the girl are on opposite sides of the
   bird. Find the distance of bird from the girl.

4. A statue, 1.6 m tall, stands on a top of pedestal, from a point on the ground, the
angle of elevation of the top of statue is 60° and from the same point the angle of
elevation of the top of the pedestal is 45 °. Find the height of the pedestal..

5.As observed from the top of a 75 m 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.

6.Astraight highway leads to the foot of a tower. A man standing at the       top of the tower observes a car at an angle of depression of 30°, which is approaching     the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the   car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this  point.

7.A man on cliff observes a boat an angle of depression of 300 m which is approaching the shore to the point immediately beneath the observer with a uniform speed. Six minutes later, the angle of depression of the boat is found to be 600. Find the time taken by the boat to reach the shore.

8 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 6 m.

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

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10.  A tree is broken by the storm. The top of the tree touches the ground making an angle 30° and ata distance of 30 m from the root. Find the height of the tree.

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11. A tree 12m high, is broken by the storm. The top of the tree touches the ground making an angle 60°. At what height from the bottom the tree is broken by the storm.