Question

25.
a To
A man, standing at the foot of a tower, sees the top of a building 20 metres away a
elevation of 60°. Climbing to the top of the tower, he sees it at an elevation of 45°
(a) Draw a rough figure based on the above facts.
(b) What is the height of the building?
(c) Calculate the height of the tower.
(Take 13 = 1.73)​

Answer 1

$a) Figure \: attached \:above$

$Height \:of \: the \: tower = AB ,\\Height \:of \:the \: building = AC ,\\Distance \: between \: foot \:of \:the \: building \:to \:tower = BC = 20\:m$

$\angle {CBE} = 60\degree , \: and \: \angle {EAD} = 45\degree$

$b) In \: \triangle EBC , \\tan \angle {CBE} = \frac{CE}{CB}$

$\implies tan 60\degree = \frac{CE}{20}$

$\implies \sqrt{3} = \frac{CE}{20}$

$\implies CE = 20\sqrt{3}$

$\implies CE = 20\times 1.73 = 34.6\:m$

$c) In \: \triangle EAD , \\tan \angle {EAD} = \frac{ED}{AD}$

$\implies tan 45\degree = \frac{ED}{20}$

$\implies 1 = \frac{ED}{20}$

$\implies ED = 20 \:m$

$Now, Height \:of \:the \:Tower AB= DC \\= CE - ED \\= 34.6 \:m - 20 \:m \\= 14.6 \:m$

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