J P Mohindru and Bharat Mohindru Solutions for Chapter: Some Applications of Trigonometry, Exercise 4: CHAPTER TEST

A $1.5 \mathrm{m}$ tall boy stands at a distance of $3 \mathrm{m}$ from the lamp-post and casts a shadow of $4.5 \mathrm{m}$ on the ground. Find the height of the lamp-post.

The angles of depression of the top and the bottom of a building $50 \mathrm{m}$ high as observed from the top of a tower are $30°$ and $60°$ respectively. Find the height of the tower and also the horizontal distance between the building and the tower.

From a window $x \mathrm{metres}$ high above the ground in a street, the angles of elevation and depression of the top and foot of the other house on the opposite side of the street are $\alpha$ and $\beta$ respectively. Show that the height of the opposite house is $x(1+\tan \alpha cot\beta ) \mathrm{metres}$.

A man standing on the deck of a ship which is $10 \mathrm{m}$ above water-level, observes the angle of elevation of the top of a hill as $60°$ and the angle of depression of the base of the hill as $30°$. Calculate the distance of the hill from the ship and the height of the hill.

If the angles of depression of the top and bottom of a tower, as seen from the top of a $100 \mathrm{m}$ high cliff are $30°$ and $60°$ respectively. Find the height of the tower.

From an aeroplane vertically above a straight horizontal plane, the angles of depression of two consecutive kilometre stone on the opposite sides of the aeroplane are found to be $\mathrm{\alpha }$ and $\mathrm{\beta }$. Find the height of the aeroplane (in km) if $\mathrm{\alpha } \mathrm{and} \mathrm{\beta }$, both are at $45°$.

The angle of elevation and depression of the top and bottom of a lighthouse from the top of a building $60 \mathrm{m}$ are $30°$ and $60°$ respectively. Find:

i) The difference between the heights of the lighthouse and the building.

ii) Distance between the lighthouse and the building,

From a window ($h \mathrm{metres}$ high above the ground) of a house in a street, the angles of elevation and depression of the top and foot of the opposite house in the street are $\mathrm{\theta }$ and $\mathrm{\varphi }$ respectively. Show that the height of the opposite house is $h(1+\mathrm{tan\theta } \mathrm{cot\varphi }) \mathrm{metres}$