(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

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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

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

Watching from the top of a $30 \ m$ high tower,the angle of depression of a stone on the ground is found to be $45^{\circ}$. Then the distance of the stone from the base of the tower is $\ldots \ldots \ldots \ m$.

Find the angle of elevation of the sun when the shadow of a pole $h$ meters high is $\sqrt{3} h$ meters long. (in $^{\circ}$)

From a point $A$ on the ground,the angle of elevation of the top of a tower is found to be $45^{\circ}$. If the distance between point $A$ and the base of the tower is $x$ and the height of the tower is $y$,then which of the following holds true?

$A$ $4 \, m$ long ladder leans on a wall such that its lower end remains $2 \, m$ away from the base of the wall. Then,the ladder makes an angle of measure $\ldots \ldots$ with the ground. (in $^\circ$)

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