mithilesh kumar singh

33. HEIGHTS AND DISTANCES

IMPORTANT FACTS AND FORMULAE

2. Trigonometrical identities:

3. Values of T-ratios:

4. Angle of Elevation: Suppose a man from a point O looks up an object P, placed above the level of his eye. Then, the angle which the line of sight makes with the horizontal through O, is called the angle of elevation of P as seen from O.

 5. The angle of Depression: Suppose a man from a point O looks down at an object P, placed below the level of his eye, then the angle which the line of sight makes with the horizontal through O, is called the angle of depression of P as seen from O.

SOLVED EXAMPLES

Ex.1.If the height of a pole is meters and the length of its shadow is 2 meters, find the angle of elevation of the sun.

Ex.2. A ladder leaning against a wall makes an angle of 60 degrees with the ground. If the length of the ladder is 19 m, find the distance of the foot of the ladder from the wall.

Distance of the foot of the ladder from the wall = 9.5 m
Ex.3. The angle of elevation of the top of a tower at a point on the ground is 30 degree. On walking 24 m towards the tower, the angle of elevation becomes 60 degree. Find the height of the tower.

Ex.4. A man standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60 degree. When he retires 36 m from the bank, he finds the angle to be 30 degree. Find the breadth of the river.

Ex.5. A man on the top of a tower, standing on the seashore finds that a boat coming towards him takes 10 minutes for the angle of depression to change from 30 degree to 60 degree. Find the time taken by the boat to reach the shore from this position.

 
Ex 6. There are two temples, one on each bank of a river, just opposite to each other. One temple is 54 m high. From the top of this temple, the angles of depression of the top and the foot of the other temple are 30 degree and 60 degree respectively. Find the width of the river and the height of the other temple.