Telangana Board Solutions for Chapter: Applications of Trigonometry, Exercise 5: Optional Exercise

A $1.2 \mathrm{m}$ tall girl spots a balloon moving with the wind in a horizontal line at a height of $88.2 \mathrm{m}$ from the ground. The angle of elevation of the balloon from the eyes of the girl at an instant is $60°$. After some time, the angle of elevation reduces to $30°$. If the distance travelled by the balloon during the interval is $K \mathrm{m}$, then find the value of $K$ upto $3$ decimal places. $(\sqrt{3}=1.732)$

The angles of elevation of the top of a lighthouse from $3$ boats $A, B \mathrm{and} C$ in a straight line of same side of the lighthouse are $a, 2a, 3a$ respectively. If the distance between the boats $A$ and $B$ and the boats $B$ and $C$ are $x$ and $y$ meters respectively, and the height of lighthouse is $h$ metres, then find the value of $\frac{\tan a·\tan 2a}{(\tan 2a-\tan a)}$.

Inner part of a cupboard is in the cuboidal shape with its length, breadth and height in the ratio $1:\sqrt{2}:1$. If is the angle made by the longest stick which can be inserted cupboard with its base inside is $k°$ then find the value $k$.

An iron spherical ball of volume $232848 {\mathrm{cm}}^3$ has been melted and converted into a cone with the vertical angle of $120°$. What are its height and base? Use $\sqrt{3}=1.732$ and $\mathrm{\pi }=\frac{22}{7}$. (Express answer rounding off the decimal to nearest whole number)

Show that the area of an isosceles triangle is $\mathrm{A}=a^2\sin \mathrm{\theta } \cos \mathrm{\theta }$ where $a$ is the length of one of the two equal sides and $\theta$ is the measure of one of two equal angles.

A right circular cylindrical tower height $h$ and radius $r$ stands on the ground. Let $\mathrm{P}$ be a point in the horizontal plane ground and $\mathrm{ABC}$ are the semicircular edge of the top of the tower such that $\mathrm{B}$ is the point in it nearest to $\mathrm{P}$. The angles of elevation of the points $\mathrm{A}$ and $\mathrm{B}$ are $45°$ and $60°$ respectively. Show that $\frac{h}{r}=\frac{\sqrt{3}{\displaystyle (}{\displaystyle 1}{\displaystyle +}{\displaystyle \sqrt{3}}{\displaystyle )}}{2}$.