(D) Let the height of the tower be $y$ and the distance from point $A$ to the base of the tower be $x$. In the right-angled triangle formed by the tow

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(D) Let the height of the tower be $y$ and the distance from point $A$ to the base of the tower be $x$. In the right-angled triangle formed by the tower and the ground,the angle of elevation is given as $\theta = 45^{\circ}$. Using the trigonometric ratio $\tan(\theta) = \frac{\text{height}}{\text{base}}$,we have: $\tan(45^{\circ}) = \frac{y}{x}$. Since $\tan(45^{\circ}) = 1$,we get $1 = \frac{y}{x}$. Therefore,$x = y$.

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

Medium

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
$x < y$
B
$x > y$
C
$x = 2y$
D
$x = y$

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Some Applications of Trigonometry

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Mix Examples - Some Applications of Trigonometry

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Write 'True' or 'False' and justify your answer.
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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?

Similar Questions

Observing an object from the point of observation,if one gets the angle of depression,then the object under observation is.........

Watching from a point $A$ on the ground $x \ m$ away from the base of the building. The height of the building is $y$ and the angle of elevation of the top of the building is found to be $25^\circ$. Then,$\ldots \ldots \ldots \ldots .$

$A$ 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 ........... $m$.

Write 'True' or 'False' and justify your answer.$\tan \theta$ increases faster than $\sin \theta$ as $\theta$ increases for $0^\circ < \theta < 90^\circ$.

$A$ person is watching from a point $A$ on the ground,which is $x \ m$ away from the base of a building. The height of the building is $y \ m$ and the angle of elevation of the top of the building is found to be $70^\circ$. Then:

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Write 'True' or 'False' and justify your answer.
$\tan \theta$ increases faster than $\sin \theta$ as $\theta$ increases for $0^\circ < \theta < 90^\circ$.