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Question
Two vertical poles of height 9m and 14m stand on a plane ground. If the distance between their feet is 12m, find the distance between their tops.
Solution
Let the two poles be DE and AB and the distance between their bases be BE.
We have:
DE = 9 m, AB = 14 m and BE = 12 m
Draw a line parallel to BE from D, meeting AB at C.
Then, DC = 12 m and AC = 5 m
We need to find AD, the distance between their tops.
Applying Pythagoras theorem in right-angled ACD, we have:
`AD^2=AC^2+DC^2`
`AD^2=5^2+12^2=25+144=169`
`AD=sqrt169=13m`
Hence, the distance between the tops to the two poles is 13 m.
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