# R S AGGARWAL AND V AGGARWAL Solutions for Class 10 Maths Chapter 14 - Height and Distance

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## Chapter 14 - Height and Distance Ex. 14

Solution 1

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

Hence the height of the tower is

Solution 2

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

Solution 3

Solution 4

Solution 5

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Solution 8

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

In right ABS,

In right PAB,

Thus, height of the pedestal = 2m

Solution 9

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°

Let AB = h meters

And AC = H meters

Hence, the required height is

Solution 10

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°

From right angled BOA

From right angled OAC

Thus

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

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

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°

Solution 18

Solution 19

Solution 20

Solution 21

Solution 22

Solution 23

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

From right CAB, we have

Hence the height of cliff is 64 m and the distance between the cliff and the ship =

Solution 24

Solution 25

Solution 26

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

In CAB, we have

Hence the height of tower is 129.9 m

Solution 27

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

Llet AD =x, CD = y

In BDA,

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

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Solution 33

## Chapter 14 - Height and Distance MCQ

Solution 1

Solution 2

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Solution 9

Solution 10

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Solution 13

Solution 14

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Solution 24

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