(B) Let the distance between the bases of the building and the pole be $2d$. The observer is at the midpoint,so the distance from the observer to the

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(B) Let the distance between the bases of the building and the pole be $2d$. The observer is at the midpoint,so the distance from the observer to the base of the pole is $d$ and to the base of the building is $d$.For the pole of height $8 \, m$,$\tan \alpha = \frac{8}{d}$.For the building of height $11 \, m$,$\tan \beta = \frac{11}{d}$.Since $11 > 8$,it follows that $\frac{11}{d} > \frac{8}{d}$,which means $\tan \beta > \tan \alpha$.Since the angles $\alpha$ and $\beta$ are in the first quadrant,the tangent function is strictly increasing.Therefore,$\beta > \alpha$,which is equivalent to $\alpha < \beta$.

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

Medium

The height of a building is $11 \, m$ and the height of a pole is $8 \, m$. Watching from the midpoint of the line segment joining their bases,the angle of elevation of the top of the pole is $\alpha$ and that of the top of the building is $\beta$. Then,$\ldots \ldots \ldots$ holds true.

A
$\alpha = \beta$
B
$\alpha < \beta$
C
$\beta < \alpha$
D
$\alpha \leqslant \beta$

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Class 10

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Some Applications of Trigonometry

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Mix Examples - Some Applications of Trigonometry

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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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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$A$ vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height $h$. At a point on the plane,the angles of elevation of the bottom and the top of the flag staff are $\alpha$ and $\beta$,respectively. Prove that the height of the tower is $\left(\frac{h \tan \alpha}{\tan \beta-\tan \alpha}\right)$.

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In a right triangle,if the measure of one of the angles is $60^{\circ}$,then the measure of the side opposite to the angle with measure $60^{\circ}$ is $\ldots \ldots$ times the measure of the hypotenuse.

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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 $m$).

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The height of a building is $11 \, m$ and the height of a pole is $8 \, m$. Watching from the midpoint of the line segment joining their bases,the angle of elevation of the top of the pole is $\alpha$ and that of the top of the building is $\beta$. Then,$\ldots \ldots \ldots$ holds true.

Similar Questions

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 $\ldots \ldots \ldots$

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 $m$.

In a right triangle,if the measure of one of the angles is $60^{\circ}$,then the measure of the side opposite to the angle with measure $60^{\circ}$ is $\ldots \ldots$ times the measure of the hypotenuse.

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 $m$).

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