(D) Let the height of the tower be $AB = 10 \, m$ and the height of the flag-post be $BC = h \, m$. Let the point on the ground be $D$. In $\triangle

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(D) Let the height of the tower be $AB = 10 \, m$ and the height of the flag-post be $BC = h \, m$. Let the point on the ground be $D$. In $\triangle ABD$,$\tan(45^{\circ}) = \frac{AB}{AD} \implies 1 = \frac{10}{AD} \implies AD = 10 \, m$. In $\triangle ACD$,$\tan(60^{\circ}) = \frac{AC}{AD} = \frac{AB + BC}{AD}$. $\sqrt{3} = \frac{10 + h}{10} \implies 10\sqrt{3} = 10 + h$. $h = 10(\sqrt{3} - 1) \approx 10(1.732 - 1) = 10(0.732) = 7.32 \, m$. Rounding to one decimal place,the height is $7.3 \, m$.

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

Medium

There is a flag-post on the top of a $10 \, m$ high tower. From a point on the ground,the angle of elevation of the top of the tower is $45^{\circ}$ and that of the top of the flag-post is $60^{\circ}$. Find the height of the flag-post. (in $, m$)

A
$3.7$
B
$7.8$
C
$6.5$
D
$7.3$

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Some Applications of Trigonometry

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Mix Examples - Some Applications of Trigonometry

Watching from the top of a building $40 \, m$ high,the angle of depression of a moving car increases from $30^{\circ}$ to $45^{\circ}$ in some interval of time. Find the distance covered by the car in that interval of time. (in $m$)

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The angle of depression of a car parked on the road as observed from the top of a building is $60^{\circ}$. The angle of depression of that car from a window $14.6 \, m$ below the top is $45^{\circ}$. Find the distance between the car and the building (in $m$).

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The angle of elevation of the top of a tower from a certain point is $30^{\circ}$. If the observer moves $20 \, m$ towards the tower,the angle of elevation of the top increases by $15^{\circ}$. Find the height of the tower.

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From the top of a building $h$ metres high,the angle of depression of an object on the ground is $\theta$. The distance (in metres) of the object from the foot of the building is $\ldots \ldots \ldots$

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In $\Delta ABC$,$\angle B$ is a right angle. If $AC = 20$ and $BC = 10$,then $m\angle ACB = \ldots$ (in $^{\circ}$)

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There is a flag-post on the top of a $10 \, m$ high tower. From a point on the ground,the angle of elevation of the top of the tower is $45^{\circ}$ and that of the top of the flag-post is $60^{\circ}$. Find the height of the flag-post. (in $, m$)

Similar Questions

Watching from the top of a building $40 \, m$ high,the angle of depression of a moving car increases from $30^{\circ}$ to $45^{\circ}$ in some interval of time. Find the distance covered by the car in that interval of time. (in $m$)

The angle of depression of a car parked on the road as observed from the top of a building is $60^{\circ}$. The angle of depression of that car from a window $14.6 \, m$ below the top is $45^{\circ}$. Find the distance between the car and the building (in $m$).

The angle of elevation of the top of a tower from a certain point is $30^{\circ}$. If the observer moves $20 \, m$ towards the tower,the angle of elevation of the top increases by $15^{\circ}$. Find the height of the tower.

From the top of a building $h$ metres high,the angle of depression of an object on the ground is $\theta$. The distance (in metres) of the object from the foot of the building is $\ldots \ldots \ldots$

In $\Delta ABC$,$\angle B$ is a right angle. If $AC = 20$ and $BC = 10$,then $m\angle ACB = \ldots$ (in $^{\circ}$)

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