Question

two poles of heights 15m and 24 m stand on a plane ground .if distance between their feet is 12m,find the distance between their tops
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Answer 1

${ \sf{ \underline{ \red{ \underline{ \red{Question</p><p>}}}} : - }}$

• Two poles of heights 15m and 24 m stand on a plane ground .if distance between their feet is 12m,find the distance between their tops.

${ \sf{ \underline{ \red{ \underline{ \red{Given</p><p>}}}} : - }}$

• a) Two poles of heights 15m and 24 m stand on a plane ground.
• b) Distance between their feet is 12m.

${ \sf{ \underline{ \red{ \underline{ \red{Find</p><p>}}}} : - }}$

• The distance between their tops.

${ \sf{ \underline{ \red{ \underline{ \red{Solution</p><p>}}}} : - }}$

{ According to question}

Let, AB & CD be the two pole's of heights 15m and 24m respectively and they stand on a plane ground.

=> AB = 15m & CD = 24m

Let, assume that AB & CD Both are perpendicular to ground. mean's they are parallel to each other.

Construction:- E be the point on CD.

Let, AE is perpendicular to CD.

Hence we can write it as

=> AB = ED = 15cm ...... ( 1 )

=> BD = AE = 12cm ...... ( 2 )

{ According to construction }

Δ AEC is a right angle triangle.

To find length of CE

=> CE = CD - ED

=> CE = 24m - 15m { from ( 1 )}

=> CE = 9m ...... ( 3 )

Now we use Pythagoras theorem to distance between tops of poles AB & CD

{ means distance AC }

{ from ( 2 ) & ( 3 )}

=> (AC)² = (AE)² + (CE)²

=> (AC)² = ( 12 )² + ( 9 )²

=> (AC)² = 144 + 81

=> (AC)² = 225

=> AC = √225

=> AC = 15m

Hence distance between the

tops of poles is 15m .