Assignment 1

Heights and Distances

1.         The angle of elevation of the top of a hill at the foot of a tower is 600 and the angle of elevation of top of the tower from the foot of the hill is 300. If the tower is 50 m high, what is the height of the hill ?

2.         A straight highway leads to the foot of a tower of height 50 m. From the top of the tower, the angle of depression of two cars standing on the highway are 300 and 600. What is the distance between two cars and how far is each car from the tower ?

3.         From a point P on the ground, the angles of elevation of the top of 10 m tall building and of a helicopter, hovering at some  height over the top of the building, are 300 and 600, respectively. Find the height of the helicopter above the ground.

4.         The angle of elevation of the top of a tower from a point on the ground  is 300. After walking 30 m towards the tower, the angle of elevation becomes 600. What is the height of the tower ?

19.         There is a small island in the middle of a 100 m wide river and a tall tree stands on the island. P and Q are points directly opposite each other on the 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 300 and 450, find the height of the tree.

5.         The angles of depression of the top and the bottom of a 7 m tall building from the top of a tower are 450 and 600, respectively. Find the height of the tower.

6.          The angles of elevation of the top of a rock from the top and foot of a 100 m high tower are, respectively, 300 and 450. Find the height of the rock.

7.         The shadow of a tower, standing on level ground, is found to be 45 m longer when Sun’s altitude is 300 than when it was at 600. Find the height of the tower.

8.         As observed from the top of a 150 m tall light house, the angle of depression of two ships approaching it are 300 and 450. If one ship is directly behind the other, find the distance between the two ships.

9.         A flag-staff stands on the top of a 5 m high tower. From a point on the ground, the angle of elevation of the top of the flag-staff is 600 and from the same point, the angle of elevation of the top of tower is 450. Find the height of the flag-staff.

10.         The angles of elevation of the top  of a tower from two points P and Q at distance of a and b, respectively, from the base and in the same straight line with it are complementary. Prove that the height of the tower is  .

11.         An aeroplane when flying at a height of 4000 m from the ground passes vertically above another aeroplane at an instant when the angles of elevation of the two planes from the same point on the ground are 600 and 450 respectively. Find the vertical distance between the aeroplanes at that instant.

12.         A tree breaks due to the storm and the broken part bends so that the top of the tree touches the ground at an angle of 300 with the ground. The distance from the foot of the tree to the point where the top touches the ground is 10 meters. Find the height of the tree.