Embibe Experts Solutions for Chapter: Some Applications of Trigonometry, Exercise 1: Exercise

Gadisar Lake is located in the Jaisalmer district of Rajasthan. It was built by the King of Jaisalmer and rebuilt by Gadsi Singh in ${14}^{\mathrm{th}}$ century. The Lake has many Chhatris. One of them is shown below:

Observe the picture. From a point on the ground level $\left(A\right)$,  $h \mathrm{m}$ above the water surface, the angle of elevation to the top of Chhatri $\left(B\right)$ is $45°$ and angle of depression to its reflection in water $\left(C\right)$ is $60°$. The height of Chhatri from the water surface is $10 \mathrm{m}$. 

What is the height $\left(h\right)$ of the point $A$ above water level ? (Use $\sqrt{3}=1.73$)

Three strong cables are used to brace a $20 \mathrm{m}$ tall pole against movement due to the wind. Each rope is attached so that the angle of elevation to the top of the pole is $60°$. Find the total length of the cable. (Round off the correct answer to the nearest whole number).

An aeroplane takes off from the ground at an angle of $27°$ and its average speed in the first $10$ seconds is $200 \mathrm{km}/\mathrm{h}$. What is altitude of the plane at the end of this time? Take $\sin 27°=0.45$

A coastal radar station picks up a distress call from a ship. It is $50 \mathrm{km}$ away $15° \mathrm{NW}$, with respect to the North. The radar station contacts a lifeboat at sea which is $20 \mathrm{km}$ away $40° \mathrm{SW}$, with respect to the South.

Find the distance of lifeboat from the ship.

The interior angles of the triangular swimming pool below are $80°, 60°,$ and $40°$. A place for pedestal $\left(P\right)$ marked in the middle of the pool, $5 \mathrm{m}$ away from each of its vertices.

Find the perimeter of the pool.

The figure below shows the separation between two high tension overhead electrical cables. The cables are sketched on graph sheet as shown below. Using the data in the figure, find the separation between the cables, if the units used are in metres. (Write the correct answer up to $2$ decimal points).

A child made a kite as in the figure below. Its unequal sides are $10 \mathrm{cm}$ and $4 \mathrm{cm}$ and $\angle D$ is $40°$. Find $\angle B$.

(Note: $\sin 40=0.64, \sin 20=0.34, \cos 40=0.77, \cos 20=0.94, \sin 58°=0.85, \cos 32°=0.85$)

A block of mass $m$ is resting on a horizontal plane is gradually inclined. As shown in the figure below, the frictional force $\left(f_s\right)$ balances the force due to gravity $(mg \sin \theta )$ on the block as the plane being inclined. Find, the maximum inclination $\left(\theta \right)$ beyond which the block starts to slide, given that, $f_s= \mu (mg \cos \theta )$, where $\mu =\frac{1}{\sqrt{3}}$, the coefficient of friction between the two surfaces, $g$ is the acceleration due to gravity.