(A) Let the height of the tower be $H$ and the distance from the foot be $d$. From the first point,we have $\tan(30^\circ) = H/d$,so $H = d \tan(30^\c

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(A) Let the height of the tower be $H$ and the distance from the foot be $d$. From the first point,we have $\tan(30^\circ) = H/d$,so $H = d \tan(30^\circ) = d/\sqrt{3}$. From the second point at height $h$ above the first,the angle of depression to the foot of the tower is $60^\circ$. This implies $\tan(60^\circ) = h/d$,so $d = h/\tan(60^\circ) = h/\sqrt{3}$. Substituting $d$ into the expression for $H$: $H = (h/\sqrt{3}) / \sqrt{3} = h/3$. Thus,the height of the tower is $h/3$.

Class 11 Mathematics Trigonometrical Equations Height and Distance

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$A$ tower subtends an angle of $30^\circ$ at a point distant $d$ from the foot of the tower and on the same level as the foot of the tower. At a second point $h$ vertically above the first,the angle of depression of the foot of the tower is $60^\circ$. The height of the tower is:

A
$h/3$
B
$h/3d$
C
$3h$
D
$3h/d$

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Trigonometrical Equations

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Height and Distance

$A$ flag is standing vertically on a tower of height $1 \ m$. At a point at a distance $2 \ m$ from the foot of the tower,the flag and the tower subtend equal angles. The height of the flag is (in meters):

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$A$ house subtends a right angle at the window of an opposite house and the angle of elevation of the window from the bottom of the first house is $60^\circ$. If the distance between the two houses is $6 \ m$,then the height of the first house is:

Medium

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If the angles of elevation of the top of a tower from three collinear points $A, B$ and $C$ on a line leading to the foot of the tower are $30^o, 45^o$ and $60^o$ respectively,then the ratio $AB : BC$ is:

DifficultJEE MAIN 2015

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An observer on the top of a tree finds the angle of depression of a car moving towards the tree to be $30^\circ$. After $3 \text{ minutes}$,this angle becomes $60^\circ$. After how much more time will the car reach the tree? (in minutes)

Medium

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$A$ man from the top of a $100 \ m$ high tower sees a car moving towards the tower at an angle of depression of $30^\circ$. After some time,the angle of depression becomes $60^\circ$. The distance (in meters) travelled by the car during the time is

MediumIIT 2001

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$A$ tower subtends an angle of $30^\circ$ at a point distant $d$ from the foot of the tower and on the same level as the foot of the tower. At a second point $h$ vertically above the first,the angle of depression of the foot of the tower is $60^\circ$. The height of the tower is:

Similar Questions

$A$ flag is standing vertically on a tower of height $1 \ m$. At a point at a distance $2 \ m$ from the foot of the tower,the flag and the tower subtend equal angles. The height of the flag is (in meters):

$A$ house subtends a right angle at the window of an opposite house and the angle of elevation of the window from the bottom of the first house is $60^\circ$. If the distance between the two houses is $6 \ m$,then the height of the first house is:

If the angles of elevation of the top of a tower from three collinear points $A, B$ and $C$ on a line leading to the foot of the tower are $30^o, 45^o$ and $60^o$ respectively,then the ratio $AB : BC$ is:

An observer on the top of a tree finds the angle of depression of a car moving towards the tree to be $30^\circ$. After $3 \text{ minutes}$,this angle becomes $60^\circ$. After how much more time will the car reach the tree? (in minutes)

$A$ man from the top of a $100 \ m$ high tower sees a car moving towards the tower at an angle of depression of $30^\circ$. After some time,the angle of depression becomes $60^\circ$. The distance (in meters) travelled by the car during the time is

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