Jitender Gupta and Divya Malik Solutions for Exercise 3: CHALLENGERS

A tower stands at the centre of a circular park. If $A$ and $B$ are the two points on the boundary of the park such that $AB=a \mathrm{m}$ subtends an angle of $60°$at the foot of the tower and the angle of elevation of the top of the tower from $A$ or $B$ is $30°$, then the height of the tower is

Find the horizontal distance between $BA$ and $CD$

In the given figure, from the top of a building $AB$, $60 \mathrm{m}$ high, the angles of depression of the top and the bottom of a vertical lamp-post $CD$ are observed to be $30°$ and $60°$, respectively. The height of the lamp-post $CD$ is $k \mathrm{m}$. Find $k$.

In the given figure, from the top of a building $AB$, $60 \mathrm{m}$ high, the angles of depression of the top and the bottom of a vertical lamp-post $CD$ are observed to be $30°$ and $60°$, respectively. Find the radius of the circle, if $y‐$axis and $AB$ are the tangent to the circle.

First, plot the points $A\left(2, 4\right), B\left(6, 4\right), C\left(6, 2\right)$ and $D\left(2, 2\right)$ and join all adjacent points. A pole $BE$ of height $h$ is standing on point $B$. If angle of elevation of the top of a pole from point $A$ is $30°$ , then find the total area formed by the figure in ${\mathrm{m}}^2$.

If the angle of elevation of a cloud from a point $h \mathrm{m}$ above a lake is $\alpha$ and the angle of depression of its reflection in the lake is $\beta$, then the height of the cloud is

A ladder rests against a vertical wall at an inclination $\alpha$ to the horizontal. If its foot is pulled away the wall through a distance $p$, so that its upper end slides at distance $q$ down the wall and the ladder makes an angle $\mathrm{\beta }$ to the horizontal, then $\frac{\cos \mathrm{\beta }-\cos \mathrm{\alpha }}{\sin \mathrm{\alpha }-\sin \mathrm{\beta }}$ is equal to

The base of a cliff is circular. From the extremities of a diameter of the base, angles of elevation of the top of the cliff are ${30}^0$ and ${60}^0$, respectively. If the height of the cliff is $500 \mathrm{m}$, then the diameter of the base of the cliff will be