(C) Let the height of the cliff be $H$ and the distance between the cliff and the tower be $d$. Let the height of the tower be $h = 50 \, m$.From the

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(C) Let the height of the cliff be $H$ and the distance between the cliff and the tower be $d$. Let the height of the tower be $h = 50 \, m$.From the base of the cliff,the angle of elevation to the top of the tower is $30^{\circ}$. Thus,$\tan(30^{\circ}) = \frac{h}{d} \implies \frac{1}{\sqrt{3}} = \frac{50}{d} \implies d = 50\sqrt{3} \, m$.From the top of the cliff,the angle of depression to the base of the tower is $60^{\circ}$. Thus,$\tan(60^{\circ}) = \frac{H}{d} \implies \sqrt{3} = \frac{H}{50\sqrt{3}}$.Solving for $H$,we get $H = 50\sqrt{3} \times \sqrt{3} = 50 \times 3 = 150 \, m$.

Class 10 Mathematics Some Applications of Trigonometry Mix Examples - Some Applications of Trigonometry

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The angle of depression of the base of a tower from the top of a cliff is $60^{\circ}$ and the angle of elevation of the top of the tower from the base of the cliff is $30^{\circ}$. If the height of the tower is $50 \, m$,find the height of the cliff in meters.

A
$336$
B
$241$
C
$150$
D
$196$

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Some Applications of Trigonometry

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Mix Examples - Some Applications of Trigonometry

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The height of a tower is $60 \, m$. From a point on the ground,the angle of elevation of the top of the tower is found to be $60^{\circ}$. Find the distance of that point from the base of the tower. (in $m$)

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The angle of depression of the base of a tower from the top of a cliff is $60^{\circ}$ and the angle of elevation of the top of the tower from the base of the cliff is $30^{\circ}$. If the height of the tower is $50 \, m$,find the height of the cliff in meters.

Similar Questions

$A$ $10\,m$ long ladder is placed in such a manner that its lower end remains $5\,m$ away from the base of a wall. Find the angles made by the ladder with the wall and with the floor.

From a point $A$,$h \text{ m}$ above the ground level,the angle of elevation of the top of a tower is $\alpha$ and the angle of depression of the base of the tower is $\beta$. Prove that the height of the tower is $\frac{h(\tan \alpha + \tan \beta)}{\tan \beta} \text{ m}$.

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