(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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Trigonometrical Equations

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Height and Distance

If the angles of elevation of the top of a tower from three collinear points $A, B$ and $C$ on a line leading to the foot of the tower are $30^o, 45^o$ and $60^o$ respectively,then the ratio $AB : BC$ is:

DifficultJEE MAIN 2015

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If the angles of elevation of two towers from the middle point of the line joining their feet are $60^\circ$ and $30^\circ$ respectively,then the ratio of their heights is

Easy

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$A$ tower,of $x$ metres high,has a flagstaff at its top. The tower and the flagstaff subtend equal angles at a point distant $y$ metres from the foot of the tower. Then,the length of the flagstaff (in metres) is:

DifficultTS EAMCET 2005

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The angle of elevation of the top of a tower from a point $A$ due south of the tower is $\alpha$ and from a point $B$ due east of the tower is $\beta$. If $AB = d$,then the height of the tower is

Medium

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$A$ sphere with centre $O$ sits on the top of a pole as shown in the figure. An observer on the ground is at a distance $50 \ m$ from the foot of the pole. She notes that the angles of elevation from the observer to points $P$ and $Q$ on the sphere are $30^{\circ}$ and $60^{\circ}$,respectively. Then,the radius of the sphere in metres is

KVPY 2016

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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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If the angles of elevation of the top of a tower from three collinear points $A, B$ and $C$ on a line leading to the foot of the tower are $30^o, 45^o$ and $60^o$ respectively,then the ratio $AB : BC$ is:

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