(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

The angle of elevation of the top of the tower observed from each of the three points $A, B, C$ on the ground,forming a triangle,is the same angle $\alpha$. If $R$ is the circum-radius of the $\Delta ABC$,then the height of the tower is

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An eagle flying $100 \ m$ above the ground looks at its prey on the ground at an angle of depression of $30^\circ$. After flying a distance of $'x' \ m$ towards the prey at the same height,the angle of depression becomes $45^\circ$. The value of $x$ will be:

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Two vertical poles of heights $20 \ m$ and $80 \ m$ stand apart on a horizontal plane. The height (in meters) of the point of intersection of the lines joining the top of each pole to the foot of the other,from this horizontal plane is:

DifficultJEE MAIN 2019

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In a triangular park $PQR$,$PQ = PR = 200 \ m$. $A$ $TV$ tower stands at the mid-point $M$ of $QR$. If the angles of elevation of the top of the tower at $P, Q,$ and $R$ are $45^o, 30^o,$ and $30^o$ respectively,then the height of the tower (in $m$) is:

DifficultJEE MAIN 2018

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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.....$m$

MediumIIT 1975

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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

The angle of elevation of the top of the tower observed from each of the three points $A, B, C$ on the ground,forming a triangle,is the same angle $\alpha$. If $R$ is the circum-radius of the $\Delta ABC$,then the height of the tower is

An eagle flying $100 \ m$ above the ground looks at its prey on the ground at an angle of depression of $30^\circ$. After flying a distance of $'x' \ m$ towards the prey at the same height,the angle of depression becomes $45^\circ$. The value of $x$ will be:

Two vertical poles of heights $20 \ m$ and $80 \ m$ stand apart on a horizontal plane. The height (in meters) of the point of intersection of the lines joining the top of each pole to the foot of the other,from this horizontal plane is:

In a triangular park $PQR$,$PQ = PR = 200 \ m$. $A$ $TV$ tower stands at the mid-point $M$ of $QR$. If the angles of elevation of the top of the tower at $P, Q,$ and $R$ are $45^o, 30^o,$ and $30^o$ respectively,then the height of the tower (in $m$) 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.....$m$

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