(C) Let $X$ be the height of building $PQ$ and $Y$ be the height of building $SR$. Let $QR$ be the distance between the bases of the two buildings.In

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Height of $X$ is greater than $Y$

(C) Let $X$ be the height of building $PQ$ and $Y$ be the height of building $SR$. Let $QR$ be the distance between the bases of the two buildings.In right-angled $\Delta SQR$,$\tan(45^{\circ}) = \frac{SR}{QR} = \frac{Y}{QR}$.Since $\tan(45^{\circ}) = 1$,we have $Y = QR$.In right-angled $\Delta PQR$,$\tan(65^{\circ}) = \frac{PQ}{QR} = \frac{X}{QR}$.Since $\tan(65^{\circ}) > 1$,we have $\frac{X}{QR} > 1$,which implies $X > QR$.Since $Y = QR$ and $X > QR$,it follows that $X > Y$.Therefore,the height of building $X$ is greater than the height of building $Y$.

Class 10 Mathematics Some Applications of Trigonometry Heights and Distances

Medium

The angle of elevation of building $Y$ from the bottom of building $X$ is $45^{\circ}$ and the angle of elevation of building $X$ from the bottom of building $Y$ is $65^{\circ}.$ Then:

A
Height of $Y$ is greater than $X$
B
Height of $X$ and $Y$ are same
C
Height of $X$ is greater than $Y$
D
We cannot say anything about the heights of $X$ and $Y$

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Some Applications of Trigonometry

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Heights and Distances

There is a slope making an angle of measure $30^{\circ}$ with the ground level. $A$ man walks on the slope for $x \, m$ and reaches a point at a height of $y \, m$ from the ground. Then,which of the following holds true?

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The angle of elevation of the top of a vertical tower from a point on the ground is $60^{\circ}$. From another point $10 \, m$ vertically above the first,its angle of elevation is $45^{\circ}$. Find the height of the tower.

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From the top of a tower,the angles of depression of two vehicles on the same side of the tower are found to be $\alpha$ and $\beta$ $(\alpha > \beta)$. If the distance between the vehicles is $b$,show that the height of the tower is $\frac{b \tan \alpha \tan \beta}{\tan \alpha - \tan \beta}$.

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During a storm,a $21 \,m$ high tree breaks but the broken part remains attached to the trunk and makes an angle of $30^{\circ}$ with the ground. At what height from the ground is the tree broken? (in $m$)

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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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The angle of elevation of building $Y$ from the bottom of building $X$ is $45^{\circ}$ and the angle of elevation of building $X$ from the bottom of building $Y$ is $65^{\circ}.$ Then:

Similar Questions

There is a slope making an angle of measure $30^{\circ}$ with the ground level. $A$ man walks on the slope for $x \, m$ and reaches a point at a height of $y \, m$ from the ground. Then,which of the following holds true?

The angle of elevation of the top of a vertical tower from a point on the ground is $60^{\circ}$. From another point $10 \, m$ vertically above the first,its angle of elevation is $45^{\circ}$. Find the height of the tower.

From the top of a tower,the angles of depression of two vehicles on the same side of the tower are found to be $\alpha$ and $\beta$ $(\alpha > \beta)$. If the distance between the vehicles is $b$,show that the height of the tower is $\frac{b \tan \alpha \tan \beta}{\tan \alpha - \tan \beta}$.

During a storm,a $21 \,m$ high tree breaks but the broken part remains attached to the trunk and makes an angle of $30^{\circ}$ with the ground. At what height from the ground is the tree broken? (in $m$)

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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