(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

$A$ tower of height $b$ subtends an angle $\alpha$ at a point $O$ on the level of the foot of the tower and at a distance $a$ from the foot of the tower. If a pole of height $p$ mounted on the tower also subtends an equal angle $\alpha$ at $O$,the height of the pole $p$ is:

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$A$ ladder rests against a wall so that its top touches the roof of the house. If the ladder makes an angle of $60^{\circ}$ with the horizontal and the height of the house is $6\sqrt{3} \text{ m}$,then the length of the ladder is ..... $m$.

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$ABCD$ is a rectangular field. $A$ vertical lamp post of height $12\,m$ stands at the corner $A$. If the angle of elevation of its top from $B$ is $60^\circ$ and from $C$ is $45^\circ$,then the area of the field is

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$A$ person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is $60^\circ$. When he moves $40 \ m$ away from the bank,he finds the angle to be $30^\circ$. The breadth of the river is.....$m$

MediumAIEEE 2004

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The angle of elevation of an object from a point $P$ on the level ground is $\alpha$. Moving $d$ metres on the ground towards the object, the angle of elevation is found to be $\beta$. Then the height (in metres) of the object is

DifficultAP EAMCET 2007

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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

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$A$ tower of height $b$ subtends an angle $\alpha$ at a point $O$ on the level of the foot of the tower and at a distance $a$ from the foot of the tower. If a pole of height $p$ mounted on the tower also subtends an equal angle $\alpha$ at $O$,the height of the pole $p$ is:

$A$ ladder rests against a wall so that its top touches the roof of the house. If the ladder makes an angle of $60^{\circ}$ with the horizontal and the height of the house is $6\sqrt{3} \text{ m}$,then the length of the ladder is ..... $m$.

$ABCD$ is a rectangular field. $A$ vertical lamp post of height $12\,m$ stands at the corner $A$. If the angle of elevation of its top from $B$ is $60^\circ$ and from $C$ is $45^\circ$,then the area of the field is

$A$ person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is $60^\circ$. When he moves $40 \ m$ away from the bank,he finds the angle to be $30^\circ$. The breadth of the river is.....$m$

The angle of elevation of an object from a point $P$ on the level ground is $\alpha$. Moving $d$ metres on the ground towards the object, the angle of elevation is found to be $\beta$. Then the height (in metres) of the object is

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