An observer in a boat finds that the angle of | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the height of the cliff be $h \ m$ and the distance of the observer from the base of the cliff be $x \ m$.From the given information,the heigh

Vedclass · Accepted Answer

$30$

Vedclass · Answer

(A) Let the height of the cliff be $h \ m$ and the distance of the observer from the base of the cliff be $x \ m$.From the given information,the height of the tower is $60 \ m$.In the right-angled triangle formed by the cliff and the observer,we have:$	an(30^\circ) = \frac{h}{x} \Rightarrow x = h \cot(30^\circ) = h\sqrt{3}$.In the right-angled triangle formed by the tower and the cliff together,the total height is $(h + 60) \ m$:$	an(60^\circ) = \frac{h + 60}{x} \Rightarrow x = \frac{h + 60}{	an(60^\circ)} = \frac{h + 60}{\sqrt{3}}$.Equating the two expressions for $x$:$h\sqrt{3} = \frac{h + 60}{\sqrt{3}}$$3h = h + 60$$2h = 60$$h = 30 \ m$.

An observer in a boat finds that the angle of elevation of the top of a tower standing on the top of a cliff is $60^\circ$ and that of the top of the cliff is $30^\circ$. If the height of the tower is $60 \ m$,then the height of the cliff is ... $m$.

Similar Questions

The angle of elevation of a stationary cloud from a point $2500 \ m$ above a lake is $15^{\circ}$ and from the same point the angle of depression of its reflection in the lake is $45^{\circ}$. The height (in metres) of the cloud above the lake, given that $\cot 15^{\circ}=2+\sqrt{3}$, is

In the figure,$\theta_1+\theta_2=\frac{\pi}{2}$ and $\sqrt{3}(BE)=4(AB)$. If the area of $\triangle CAB$ is $2\sqrt{3}-3 \text{ unit}^2$,when $\frac{\theta_2}{\theta_1}$ is the largest,then the perimeter (in unit) of $\triangle CED$ is equal to $...........$.

$A$ tower $50 \ m$ high stands on the top of a mount. From a point on the ground,the angles of elevation of the top and bottom of the tower are found to be $75^o$ and $60^o$ respectively. The height of the mount is:

$A$ tower subtends an angle of $30^\circ$ at a point distant $d$ from the foot of the tower and on the same level as the foot of the tower. At a second point $h$ vertically above the first,the angle of depression of the foot of the tower is $60^\circ$. The height of the tower is:

$ABCD$ is a rectangular field. $A$ vertical lamp post of height $12\,m$ stands at the corner $A$. If the angle of elevation of its top from $B$ is $60^\circ$ and from $C$ is $45^\circ$,then the area of the field is

Vedclass Test Series

Exam Paper Generator

Online Exam Module