Two poles of height \[13\,m\] and \[7\,m\] respectively stand vertically on a plane ground at a distance of \[8\,m\] from each other. The distance between their tops is: |
A) \[9\,m\]
B) \[10\,m\]
C) \[11\,m\]
D) \[12\,m\]
Correct Answer: B
Solution :
[b] Let AB and CD be the poles such that \[AB=13\,m,\] \[CD=7\,m\] |
and \[CA=8m.\] |
Draw \[DE\bot AB\]. |
Then, \[AE=CD=7m,\] \[BE=6m\] |
and \[DE=8m.\] |
In right \[\Delta BDE,\] by Pythagoras theorem |
\[B{{D}^{2}}=B{{E}^{2}}+D{{E}^{2}}={{6}^{2}}+{{8}^{2}}\] |
\[=36+64=100\] |
\[\Rightarrow \,\,\,\,\,\,\,\,BD=\sqrt{100}=10m.\] |
Hence, the distance between their tops is \[10m\]. |
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