(B) Let $h$ be the height of the house and $H$ be the height of the tower above the top of the house.From the triangle formed by the angle of depressi

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(B) Let $h$ be the height of the house and $H$ be the height of the tower above the top of the house.From the triangle formed by the angle of depression,we have $\tan(30^\circ) = \frac{h}{12}$.Thus,$h = 12 \tan(30^\circ) = 12 \times \frac{1}{\sqrt{3}} = 4\sqrt{3} \ m$.From the triangle formed by the angle of elevation,we have $\tan(60^\circ) = \frac{H}{12}$.Thus,$H = 12 \tan(60^\circ) = 12 \sqrt{3} \ m$.The total height of the tower is $h + H = 4\sqrt{3} + 12\sqrt{3} = 16\sqrt{3} \ m$.

Class 11 Mathematics Trigonometrical Equations Height and Distance

Medium

The angle of elevation of the top of a tower from the top of a house is $60^\circ$ and the angle of depression of its base is $30^\circ$. If the horizontal distance between the house and the tower is $12 \ m$,then the height of the tower is

A
$48 \ \sqrt{3} \ m$
B
$16 \ \sqrt{3} \ m$
C
$24 \ \sqrt{3} \ m$
D
$16 / \sqrt{3} \ m$

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Trigonometrical Equations

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Height and Distance

The top of a hill observed from the top and bottom of a building of height $h$ is at the angle of elevation $p$ and $q$ respectively. The height of the hill is

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The angle of elevation of the top of a pillar at a point $A$ on the ground is $15^\circ$. On walking $40 \ m$ towards the pillar,the angle becomes $30^\circ$. The height of the pillar is $... \ m$.

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The shadow of a tower is found to be $60 \ m$ shorter when the sun's altitude changes from $30^{\circ}$ to $60^{\circ}$. The height of the tower from the ground is approximately equal to......$m$

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$A$ ladder $5 \ m$ long leans against a vertical wall. The bottom of the ladder is $3 \ m$ from the wall. If the bottom of the ladder is pulled $1 \ m$ farther from the wall,how much does the top of the ladder slide down the wall?

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If the angle of elevation of the top of a tower at a distance of $500 \, m$ from its foot is $30^\circ$,then the height of the tower is:

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The angle of elevation of the top of a tower from the top of a house is $60^\circ$ and the angle of depression of its base is $30^\circ$. If the horizontal distance between the house and the tower is $12 \ m$,then the height of the tower is

Similar Questions

The top of a hill observed from the top and bottom of a building of height $h$ is at the angle of elevation $p$ and $q$ respectively. The height of the hill is

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