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

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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

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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°

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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 =

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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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Chapter 14 - Height and Distance MCQ

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