(B) Let the height of the tower be $h$ and the breadth of the river be $x$. According to the problem,the angle of elevation is $45^\circ$. Using the t

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Breadth of the river and the height of the tower are the same

(B) Let the height of the tower be $h$ and the breadth of the river be $x$. According to the problem,the angle of elevation is $45^\circ$. Using the trigonometric ratio,$\tan(45^\circ) = \frac{\text{height of tower}}{\text{breadth of river}} = \frac{h}{x}$. Since $\tan(45^\circ) = 1$,we have $1 = \frac{h}{x}$,which implies $x = h$. Therefore,the breadth of the river and the height of the tower are the same.

Class 11 Mathematics Trigonometrical Equations Height and Distance

Medium

$A$ person standing on the bank of a river finds that the angle of elevation of the top of a tower on the opposite bank is $45^\circ$. Which of the following statements is correct?

A
Breadth of the river is twice the height of the tower
B
Breadth of the river and the height of the tower are the same
C
Breadth of the river is half of the height of the tower
D
None of the above

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$A$ person standing on the bank of a river finds that the angle of elevation of the top of a tower on the opposite bank is $45^\circ$. Which of the following statements is correct?

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$A$ pole stands vertically inside a triangular park $\Delta ABC$. Let the angle of elevation of the top of the pole from each corner of the park be $\frac{\pi}{3}$. If the radius of the circumcircle of $\Delta ABC$ is $2$,then the height of the pole is equal to:

In a triangular park $PQR$,$PQ = PR = 200 \ m$. $A$ $TV$ tower stands at the mid-point $M$ of $QR$. If the angles of elevation of the top of the tower at $P, Q,$ and $R$ are $45^o, 30^o,$ and $30^o$ respectively,then the height of the tower (in $m$) is:

$A$ vertical pole subtends an angle $\tan ^{-1}\left(\frac{1}{2}\right)$ at a point $P$ on the ground. If the angles subtended by the upper half and the lower half of the pole at $P$ are respectively $\alpha$ and $\beta$, then $(\tan \alpha, \tan \beta)$ is equal to

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