## RS Aggarwal Solutions Class 10 Chapter 14 Height and Distance Ex 14a

These Solutions are part of RS Aggarwal Solutions Class 10. Here we have given RS Aggarwal Solutions Class 10 Chapter 14 Height and Distance Ex 14a.

**Other Exercises**

- RS Aggarwal Solutions Class 10 Chapter 14 Height and Distance Ex 14a
- RS Aggarwal Solutions Class 10 Chapter 14 Height and Distance MCQ

**Question 1.**

**A tower stands vertically on the ground. From a point on the ground which is 20 m away from the foot of the tower, the angle of elevation of its top is found to be 60°. Find the height of the tower.**

**Solution:
**Let AB be the tower standing on a level ground and O be the position of the observer. Then OA = 20 m and ∠OAB = 90° and ∠AOB = 60°

Let AB = h meters

From the right ∆OAB, we have

**Question 2.**

**A kite is flying at a height of 75 m from the level ground, attached to a string inclined at a 60° to the horizontal. Find the length of the string assuming that there is no slack in it.**

**Solution:
**Let OB be the length of the string from the level of ground and O be the point of the observer, then, AB = 75m and ∠OAB = 90° and ∠AOB = 60°, let OB = l meters.

From the right ∆OAB, we have

**Question 3.**

**An observer 1.5 m tall is 30 m away from a chimney. The angle of elevation of the top of the chimney from his eye is 60°. Find the height of the chimney. [CBSE 2013C]**

**Solution:
**

**Question 4.**

**The angles of elevation of the top of a tower from two points at distances of 5 metres and 20 metres from the base of the tower and in the same straight line with it, are complementary. Find the height of the tower. [CBSE 2014]**

**Solution:
**

**Question 5.**

**The angle of elevation of the top of a tower at a distance of 120 m from a point A on the ground is 45°. If the angle of elevation of the top of a flagstaff fixed at the top of the tower, at A is 60°, then find the height of the flagstaff. [Use √3 = 1.732] [CBSE 2014]**

**Solution:
**

**Question 6.**

**From a point on the ground 40 m away from the foot of a tower, the angle of elevation of the top of the tower is 30°. The angle of elevation of the top of a water tank (on the top of the tower) is 45°. Find (i) the height of the tower, (ii) the depth of the tank.**

**Solution:
**

**Question 7.**

**A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height 6 m. At a point on the plane, the angle of elevation of the bottom of the flagstaff is 30° and that of the top of the flagstaff is 60°. Find the height of the tower. [Use √3 = 1.732] [CBSE 2011]**

**Solution:
**

**Question 8.**

**A statue 1.46 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the 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. [Use √3=1.73]**

**Solution:
**Let SP be the statue and PB be the pedestal. Angles of elevation of S and P are 60° and 45° respectively.

Further suppose AB = x m, PB = h m

**Question 9.**

**The angle of elevation of the top of an unfinished tower at a distance of 75 m form its base is 30°. How much higher must the tower be raised so that the angle of elevation of its top at the same point may be 60°?**

**Solution:
**Let AB be the unfinished tower and let AC be complete tower.

Let O be the point of observation. Then,

OA = 75 m

∠AOB = 30° and ∠AOC = 60°

**Question 10.**

**On a horizontal plane there is a vertical tower with a flagpole on the top of the tower. At a point, 9 metres away from the foot of the tower, the angle of elevation of the top of bottom of the flagpole are 60° and 30° respectively. Find the height of the tower and the flagpole mounted on it. [Use √3=1.73]**

**Solution:
**Let AB be the tower and BC be flagpole, Let O be the point of observation.

Then, OA = 9 m, ∠AOB = 30° and ∠AOC = 60°

Hence, height of the tower= 5.196 m and the height of the flagpole = 10.392 m.

**Question 11.**

**Two poles of equal heights are standing opposite to each other on either side of the road which is 80 m wide. From a point P between them on the road, the angle of elevation of the top of one pole is 60° and the angle of depression from the top of another pole at P is 30°. Find the height of each pole and distances of the point P from the poles. [CBSE 2015]**

**Solution:
**

**Question 12.**

**Two men are on opposite sides of a tower. they measure the angles of elevation of the top of the tower as 30° and 45° respectively. If the height of the tower is 50 metres, find the distance between the two men. [Take √3=1.732]**

**Solution:
**

**Question 13.**

**From the top of a tower 100 m high, a man observes two cars on the opposite sides of the tower with angles of depression 30° and 45°, respectively. Find the distance between the cars. [Take √3 = 1.73] [CBSE 2011]**

**Solution:
**

**Question 14.**

**A straight highway leads to the foot of a tower. A man standing on 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 form this point.**

**Solution:
**

**Question 15.**

**A TV tower stands vertically on a bank of canal. From a point on other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower and the width of the canal.**

**Solution:
**

**Question 16.**

**The angle of elevation of the top of a building from the foot of a tower is 30°. 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, then find the height of the building. [CBSE 2013]**

**Solution:
**

**Question 17.**

**The horizontal distance between two towers is 60 metres. The angle of depression of the top of the first tower when seen from the top of the second tower is 30°. If the height of the second tower is 90 metres, find the height of the first tower. [Use √3=1.732]**

**Solution:
**Let AB and CD be the first and second towers respectively.

Then, CD = 90 m and AC = 60 m.

Let DE be the horizontal line through D.

Draw BF ⊥CD,

Then, BF = AC = 60 m

∠FBD = ∠EDB = 30°

**Question 18.**

**The angle of elevation of the top of a chimney from the foot of a tower is 60° and the angle of depression of the foot of the chimney from the top of the tower is 30°. If the height of the tower is 40 metres, then find the height of the chimney.**

**According to pollution control norms, the minimum height of a smoke emitting chimney should be 100 metres. State if the height of the above mentioned chimney meets the pollution norms. What value is discussed in this ? [CBSE 2014]**

**Solution:
**

**Question 19.**

**From the top of a 7-metre-high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower. [Use √3 = 1.732] [CBSE 2013C]**

**Solution:
**

**Question 20.**

**The angle of depression from the top of a tower of a point A on the ground is 30°. On moving a distance of 20 metres from the point A towards the foot of the tower to a point B, the angle of elevation of the top of the tower from the point B is 60°. Find the height of the tower and its distance from the point A. [CBSE 2012]**

**Solution:
**

**Question 21.**

**The angle of elevation of the top of a vertical tower from a point on the ground is 60°. From another point 10 m vertically above the first, its angle of elevation is 30°. Find the height of the tower. [CBSE 2011]**

**Solution:
**

**Question 22.**

**The angles of depression of the top and bottom of a tower as seen from the top of a 60√3-m-high cliff are 45° and 60°, respectively. Find the height of the tower. [CBSE 2012]**

**Solution:
**

**Question 23.**

**A man on the deck of a ship, 16 m above water level observes that the angles of elevation and depression respectively of the top and bottom of a cliff are 60° and 30°. Calculate the distance of the cliff from the ship and height of the cliff.**

**Solution:
**Let AB be the height of the deck and let CD be the cliff..

Let the man be at B, then, AB= 16 m

Let BE ⊥CD and AE ⊥ CD

Then, ∠EBD = 60 and ∠EBC = 30

CE = AB = 16m

Let CD = h meters

Then, ED = (h 16)m

From right ∆BED, we have

**Question 24.**

**The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60°. At a point Y, 40 m vertically above X, the angle of elevation is 45°. Find the height of tower PQ. [Take √3 = 1.73] [CBSE 2003C]**

**Solution:
**

**Question 25.**

**The angle of elevation of an aeroplane from a point on the ground is 45°. After flying for 15 seconds, the elevation changes to 30°. If the aeroplane is flying at a height of 2500 metres, find the speed of the aeroplane.**

**Solution:
**

**Question 26.**

**The angle of elevation of the top of a tower from a point on the same level as the foot of the tower is 30° On advancing 150 m towards the foot of the tower, the angle of elevation becomes 60°. Show that the height of the tower is 129.9 metres.**

**Solution:
**Let AB be the tower and let the angle of elevation of its top at C be 30°.

Let D be a point at a distance 150 m from C such that the angle of elevation of the top of tower at D is 60°.

Let h m be the height of the tower and AD = x m

**Question 27.**

**As observed form the top of a lighthouse, 100 m above sea level, the angle of depression of a ship, sailing directly towards it, changes from 30° to 60°. Determine the distance travelled by the ship during the period of observation.**

**Solution:
**Let AB be the light house and let C and D be the positions of the ship.

Let AD =x, CD = y

The distance travelled by the ship during the period of observation = 115.46 m

**Question 28.**

**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 2.5 m from the banks, find width of the river.**

**Solution:
**

**Question 29.**

**The angles of elevation of the top of a tower from two points at distances of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Show that the height of the tower is 6 metres.**

**Solution:
**

**Question 30.**

**A ladder of length 6 metres makes an angle of 45° with the floor while leaning against one wall of a room. If the foot of the ladder is kept fixed on the floor and it is made to lean against the opposite wall of the room, it makes an angle of 60° with the floor. Find the distance between two walls of the room. [CBSE 2011]**

**Solution:
**

**Question 31.**

**From the top of a vertical tower, the angles of depression of two cars in the same straight line with the base of the tower, at an instant are found to be 45° and 60°. If the cars are 100 m apart and are on the same side of the tower, find the height of the tower. [CBSE 2011]**

**Solution:
**

**Question 32.**

**An electrician has to repair an electric fault on a pole of height 4 metres. He needs to reach a point 1 metre below the top of the pole to undertake the repair work. What should be the length of the ladder that he should use, which when inclined at an angle of 60° to the horizontal would enable him to reach the required position? [Use √3 = 1.73]**

**Solution:
**

**Question 33.**

**From the top of a building AB, 60 m high, the angles of depression of the top and bottom of a vertical lamp post CD are observed to be 30° and 60°, respectively. Find [CBSE 2009]**

**(i) the horizontal distance between AB and CD,**

**(ii) the height of the lamp post,**

**(iii) the difference between the heights of the building and the lamp post.**

**Solution:
**

Hope given RS Aggarwal Solutions Class 10 Chapter 14 Height and Distance Ex 14a are helpful to complete your math homework.

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