(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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$A$ cable tied to the top of an electric pole is fixed at a point on the ground. The length of the cable is $20 \, m$. If it makes an angle of $30^{\circ}$ with the ground,then the height of the electric pole is ........ (in $, m$)

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The approximate value of $\sqrt{3}$ up to $2$ decimal places is $\ldots \ldots \ldots$

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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 $, m$)

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From a balloon vertically above a straight road,the angles of depression of two cars at an instant are found to be $45^{\circ}$ and $60^{\circ}$. If the cars are $100 \, m$ apart,find the height of the balloon.

Observing from the top of a $150\, m$ high tower,the angle of depression of a cycle on the ground is found to be $60^{\circ}$. How far away is the cycle from the tower?

$A$ cable tied to the top of an electric pole is fixed at a point on the ground. The length of the cable is $20 \, m$. If it makes an angle of $30^{\circ}$ with the ground,then the height of the electric pole is ........ (in $, m$)

$A$ ladder leans on a wall to reach a height of $3 \, m$ on the wall. If the ladder makes an angle of $30^{\circ}$ with the ground,the length of the ladder is ........... $m$.

The approximate value of $\sqrt{3}$ up to $2$ decimal places is $\ldots \ldots \ldots$

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