(C) Let $\overline{AB}$ be the pole and $\overline{AC}$ be the wire fixed on the ground at point $C$.Given: $AC = 7 \, m$,$m\angle B = 90^{\circ}$,and

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(C) Let $\overline{AB}$ be the pole and $\overline{AC}$ be the wire fixed on the ground at point $C$.Given: $AC = 7 \, m$,$m\angle B = 90^{\circ}$,and $m\angle C = 30^{\circ}$.In $\Delta ABC$,we have:$\sin C = \frac{\text{Opposite side}}{\text{Hypotenuse}} = \frac{AB}{AC}$$\sin 30^{\circ} = \frac{AB}{7}$Since $\sin 30^{\circ} = \frac{1}{2}$,we have:$\frac{1}{2} = \frac{AB}{7}$$AB = \frac{7}{2} = 3.5 \, m$.Thus,the height of the pole is $3.5 \, m$.

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

Medium

$A$ pole stands erect on the ground. $A$ wire tied to the top of the pole is affixed at a point on the ground. If the length of the wire is $7 \, m$ and the wire makes an angle of $30^{\circ}$ with the ground,find the height of the pole (in $m$).

A
$8.1$
B
$6.2$
C
$3.5$
D
$5.7$

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Some Applications of Trigonometry

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Mix Examples - Some Applications of Trigonometry

$A$ $4 \, m$ 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 $^\circ$)

Medium

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The distance between two poles of equal height is $200 \, m$. From a point situated on the line segment joining their bases,the angles of elevation of their tops are found to be $60^{\circ}$ and $30^{\circ}$. Find the height of the pole in $m$.

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As observed from the top of a building,the angle of depression of a man standing $10 \, m$ away from the building is found to be $45^{\circ}$. Find the height of the building (in $m$).

Medium

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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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An erect tree is $300\, m$ away from a hill. If the height of the hill is $300\, m$,find the angle of depression of the base of the tree from the top of the hill. (in $^{\circ}$)

Medium

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$A$ pole stands erect on the ground. $A$ wire tied to the top of the pole is affixed at a point on the ground. If the length of the wire is $7 \, m$ and the wire makes an angle of $30^{\circ}$ with the ground,find the height of the pole (in $m$).

Similar Questions

$A$ $4 \, m$ 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 $^\circ$)

The distance between two poles of equal height is $200 \, m$. From a point situated on the line segment joining their bases,the angles of elevation of their tops are found to be $60^{\circ}$ and $30^{\circ}$. Find the height of the pole in $m$.

As observed from the top of a building,the angle of depression of a man standing $10 \, m$ away from the building is found to be $45^{\circ}$. Find the height of 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.

An erect tree is $300\, m$ away from a hill. If the height of the hill is $300\, m$,find the angle of depression of the base of the tree from the top of the hill. (in $^{\circ}$)

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