J P Mohindru and Bharat Mohindru Solutions for Chapter: Some Applications of Trigonometry, Exercise 1: EXERCISE

In a violent storm, a tree got bend by the wind. The top of the tree meets the ground at an angle of $30°$, at a distance of $30 \mathrm{metres}$ from the root. At what height from the bottom did the tree get bend? What was the original height of the tree?

Two men are on opposite sides of a tower. They measure the angles of elevation of the top of the tower as $30°$ and$45°$ respectively. If the height of the tower is $50 \mathrm{metres}$, find the distance between the two men.

The angle of elevation of the top of a hill from the foot of a tower is $60°$ and the angle of elevation of the top of the tower from the foot of the hill is $30°$. If the tower is $50 \mathrm{m}$ high, what is the height of the hill?

Angle of elevation of the top $\mathrm{Q}$ from point of a vertical tower $\mathrm{PQ}$ from point $\mathrm{X}$ on the ground is $60°$. At a point $\mathrm{Y}$, $40 \mathrm{m}$ vertically above $\mathrm{X}$, the angle of elevation is $45°$. Find the height of the tower $\mathrm{PQ}$.     $\left[\mathrm{Take} \sqrt{3}=1.73\right]$

The angle of elevation of an aeroplane from a point on the ground is $45°$. After flying for $15$ seconds, the elevation becomes $30°$. If the aeroplane is flying at a height of $2500 \mathrm{metres}$, find the speed of the aeroplane in $\mathrm{km}/\mathrm{hr}$.

The angle of elevation of a jet fighter from a point $\mathrm{A}$ on the ground is $60°$. After a flying of $15$ seconds, the angle of elevation changes to $30°$. If the jet is flying at a speed of $720 \mathrm{km}/\mathrm{h}$, find the height at which the jet is flying.

A boy whose eye-level is $1.3 \mathrm{m}$ from ground, spots a balloon moving with the wind in a horizontal line at some height from the ground. The angle of elevation of the balloon from the eyes of the boy at an instant is $60°$. After $2 \mathrm{seconds}$, the angle of elevation reduces to $30°$. If the speed of the wind is $29\sqrt{3} \mathrm{m}/\sec$, then find the height of the balloon from the ground.

An aeroplane was $600 \mathrm{m}$ high, passes vertically above another aeroplane at an instant when their angles of elevation at the same observing point are $60°$ and $45°$ respectively. How many metres higher is one than the other?