Question

A vertical tower stands on a horizontal plane and is surmounted by a flag staff
of height 14m. From a point on the ground the angle of elevation of bottom and
top of the flag staff are 45 and 60° respectively. Find the height of the tower
and distance of the point from the tower.
Please answer as soon as possible!​

Answer 1

Answer:

HOPE it helps ❤️❤️❤️❤️❤️❤️❤️❤️❤️

Answer 2

$\huge \bold {\underline{ \underline{ \underline{ \color{indigo}{ \: \: \: solution \: \: \: }}}}}$

$\implies \:In \: △ \: CBD, \\ \: tan \: \: 30 ° = \frac{BD}{BC}$

$\frac{1}{ \sqrt{3} } = \frac{h}{x}$

${\color{red}{x \: = \: \sqrt{3} h \: ------ 1)}}$

$⇒ In \: \: △ \: \: ABC , \\ tan \: 45° = \: \frac{AB}{AB}$

$⇒ 1= \frac{7+h}{x}$

${\color{blue}{x = 7 + h}}$

${ \color{green}{⇒ \sqrt{3} h = 7 + h \: \: \: \: \: \: [ From ( 1 ) ]}}$

$⇒ \sqrt{3} h - h = 7$

$⇒ ( \sqrt{3} - 1)h \: = 7$

$⇒ h = \frac{7}{ \sqrt{3} - 1 }$

$\bold{ \color{purple}★{ \: \: rationalise \: \: the \: \: denominator \: }}★$

$h = \frac{7}{ \sqrt{3} - 1} \times \frac{{ \sqrt{3} + 1} }{{ \sqrt{3} + 1} }$

${ \color{pink}{∴ \: h = \frac{7( \sqrt{3} + 1) }{ \sqrt{3} - 1}}} { \color{pink}= \frac{7( 1.73 + 1) }{2} }$

$\huge{ \boxed{ \color{blue}{h \: = 9.55 \: m}}}$

∴ Height of the tower is 9.55m.

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