(D) Let the tower be $AB$ with height $40 \, m$. Let the two men be at points $O_1$ and $O_2$ on opposite sides of the tower.In $\Delta O_1BA$,$\tan(4

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(D) Let the tower be $AB$ with height $40 \, m$. Let the two men be at points $O_1$ and $O_2$ on opposite sides of the tower.In $\Delta O_1BA$,$\tan(45^{\circ}) = \frac{AB}{O_1B}$ $\Rightarrow 1 = \frac{40}{x}$ $\Rightarrow x = 40 \, m$.In $\Delta O_2BA$,$\tan(30^{\circ}) = \frac{AB}{O_2B}$ $\Rightarrow \frac{1}{\sqrt{3}} = \frac{40}{y}$ $\Rightarrow y = 40\sqrt{3} \, m$.Using $\sqrt{3} \approx 1.732$,$y = 40 \times 1.732 = 69.28 \, m$.The distance between the men is $x + y = 40 + 69.28 = 109.28 \, m$.

Class 11 Mathematics Trigonometrical Equations Height and Distance

Medium

Two men are on the opposite sides of a tower. They measure the angles of elevation of the top of the tower as $45^{\circ}$ and $30^{\circ}$ respectively. If the height of the tower is $40 \, m,$ find the distance between the men.

A
$40 \, m$
B
$40\sqrt{3} \, m$
C
$68.28 \, m$
D
$109.28 \, m$

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Trigonometrical Equations

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Height and Distance

$A$ person standing at a distance of $10 \ m$ from a pole observes that the angle subtended by the lower $\frac{1}{3}$rd part and the upper $\frac{2}{3}$rd part of the pole are the same. Find the height of the pole.

Medium

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$A$ tower subtends angles $\alpha, 2 \alpha$ and $3 \alpha$ respectively at points $A, B$ and $C$, all lying on a horizontal line through the foot of the tower. Then $\frac{A B}{B C}$ is equal to:

DifficultTS EAMCET 2003

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The angle of elevation of the top of a tower from a point $A$ due south of the tower is $\alpha$ and from a point $B$ due east of the tower is $\beta$. If $AB = d$,then the height of the tower 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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$A$ flag-staff $5 \ m$ high stands on a building of height $25 \ m$. An observer at a height of $30 \ m$ observes that the flag-staff and the building subtend equal angles. The distance of the observer from the top of the flag-staff is:

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Two men are on the opposite sides of a tower. They measure the angles of elevation of the top of the tower as $45^{\circ}$ and $30^{\circ}$ respectively. If the height of the tower is $40 \, m,$ find the distance between the men.

Similar Questions

$A$ person standing at a distance of $10 \ m$ from a pole observes that the angle subtended by the lower $\frac{1}{3}$rd part and the upper $\frac{2}{3}$rd part of the pole are the same. Find the height of the pole.

$A$ tower subtends angles $\alpha, 2 \alpha$ and $3 \alpha$ respectively at points $A, B$ and $C$, all lying on a horizontal line through the foot of the tower. Then $\frac{A B}{B C}$ is equal to:

The angle of elevation of the top of a tower from a point $A$ due south of the tower is $\alpha$ and from a point $B$ due east of the tower is $\beta$. If $AB = d$,then the height of the tower is

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