CBSE Book Class 10 Maths Height and Distance

Chapter 13

Height and Distance

Height and Distance

Some times we are required to find the height of a tower, tree, building and distance of a ship from light house, width of a river etc. We cannot measure them accurately, though

we can find them using the knowledge of trigonometric ratio.

Line of sight: -

When we see an object standing on the ground. The line of sight is the line from our eye to the object, we see.

Angle of Elevation:-

When the object is above the horizontal level of our eye, we have to turn our head upwards to see an object. In this process, our eyes move through an angle which is called angle of elevation.

Angle of Depression:-

When the object is on the ground and the observer is on a building then the object is below the level of the eye of the observer. The observer has to turn his head downward to see the object. In doing so, his eyes move through an angle which is called angle of depression.

Example 1. A man is standing on the deck of a ship, which is 8m above water level. He observes the angle of elevation of the top of a hill as 60⁰ and angle of depression of the base of the hill as 30⁰. Calculate the distance of the hill from the ship and the height of the hill.

Exercise - 26

1.From the top of tower 60m high, the angles of depression of the top and bottom of a building whose base is in the same straight line with the base of the tower are observed to be 30⁰ and 60⁰ respectively. Find the height of the building.

2.An aeroplane flying horizontally at a height of .1.5 km above the ground is observed at a certain point on earth to subtend and angle of 60⁰. After 15 seconds, its angle of elevation at the same point is observed to be 30⁰. Calculate the speed of the aeroplane in km/hr.

3.A tower in a city is 750m high and a multi-storeyed hotel at the city centre is 50m high. The angle of elevation of the top of the tower at the top of the hotel is 30⁰. A building, h metres high, is situated on the straight road connecting the tower with the city centre at a distance the city centre at a distance of a 1.0 km from the tower. Find the value of h if the top of the hotel, the top of the building and the top of the tower are in a straight line. Also find the distance of the tower from the city centre.

4.In the adjoining figure, ABCD is a trapezium in which AB || CD. Line segments RS and LM are drawn parallel to AB such that AJ = JK = KP. If AB = O.5m and AP = BQ = 1.8m, find the length of AP, BD, RS and LM.

5.The angle of elevation of a jet plane from a point A on the ground is 600. After a flight of 15 seconds, the angle of elevation changes to 30⁰. If the jet plane is flying at a constant height of find the speed of the jet plane.

6.Determine the height of a mountain if the elevation if the elevation of its top at an unknown distance from the base is 45⁰ and at a distance 10km further off from the mountain, along the same line, the angle of elevation is 30⁰ (USE tan30⁰ = 0.5774).

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

8.The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60⁰. At a point Y, 40m vertically above X, the angle of elevation is 45⁰. Find the height of the tower PQ and the distance XQ.

Please refer to attached file for CBSE Class 10 Maths Height and Distance