Question

the angle of elevation of the top of a tower from a certain points is 30°. if the observer moves 20 m towards the tower,the angle of elevation of the top of the tower increases by 15°. the height of the tower is​

Answer 1

GIVEN :-

★ The angle of elevation of the top of a tower from a certain point is 30°. If the observer moves 20 m towards the tower the angle of elevation of the top of the tower increased by 15°.

TO FIND :-

• The height of the tower. AC

SOLUTION :-

Let the angle of elevation be ∅.

Here , in the figure if we will see then ,there are two right angled triangles formed.

In ∆ APC,

$\\ : \implies \displaystyle\sf \: \tan \theta \: = \dfrac{perpendicular}{base}$

$: \implies \displaystyle\sf \: \tan45 ^{ \circ} = \dfrac{AC}{PC}$

$: \implies \displaystyle\sf1 = \dfrac{AC}{PC} \: \: \: \: \: \: \: \: \: \: \: \: \: \bigg \lgroup \tan45 ^{ \circ} = 1 \bigg \rgroup$

$: \implies \displaystyle\sf AC = PC \: \: \: \: \: \: \: \: \: \: \bigg \lgroup \: Equation \ 1 \bigg \rgroup$

Now in ∆ ABC,

$\\ : \implies \displaystyle\sf \: \tan \theta \: = \dfrac{perpendicular}{base}$

$: \implies \displaystyle\sf \: \tan30 ^{ \circ} = \dfrac{AC}{BC}$

$: \implies \displaystyle\sf \dfrac{1}{ \sqrt{3} } = \dfrac{AC}{BC} \: \: \: \: \: \: \: \: \: \: \: \: \: \bigg \lgroup \tan30^{ \circ} = \dfrac{1}{ \sqrt{3} } \bigg \rgroup$

$: \implies \displaystyle\sf \dfrac{1}{ \sqrt{3} } = \dfrac{AC}{BP + PC}$

$: \implies \displaystyle\sf \dfrac{1}{ \sqrt{3} } = \dfrac{AC}{20 +AC } \: \: \: \: \: \: \: \: \: \bigg\lgroup \: \because \: Equation \ 1 \bigg\rgroup$

$: \implies \displaystyle\sf \sqrt{3} \: AC = 20 + AC$

$: \implies \displaystyle\sf \sqrt{3} \: AC -AC = 20$

$: \implies \displaystyle\sf \: AC (\sqrt{3} - 1) = 20$

$: \implies \displaystyle\sf \: AC (1.73 - 1) = 20$

$: \implies \displaystyle\sf \: AC (0.73 ) = 20$

$: \implies \displaystyle\sf \: AC = \frac{20}{0.73}$

$: \implies \displaystyle\sf \underline{ \boxed{ \sf \: \: AC \: \approx 27.39 }}$

$\therefore \underline{ \displaystyle\sf \: Height \: of \: the \: tower , AC \: is \: \: 27 . 39 \: m. \: }$

Answer 2

Answer:

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Step-by-step explanation:

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