Tamil Nadu Board Solutions for Chapter: Trigonometry, Exercise 11: Unit Exercise

The horizontal distance between two buildings is $70 \mathrm{m}$. The angle of depression of the top of the first building when seen from the top of the second building is $45°$. If the height of the second building is $120 \mathrm{m}$, find the height of the first building.

From the top of $60 \mathrm{m}$ High tower, the angles of depression of the top and bottom of a vertical lamp post are observed to be $38°$ and $60°$ respectively. Find the height of the lamp post. $\left(\tan 38°=0.7813, \sqrt{3}=1.732\right)$

An aeroplane at an altitude of $1800 \mathrm{m}$ finds that two boats are sailing towards it in the same direction. The angles of depression of the boats as observed from the aeroplane are $60°$ and $30°$ respectively. Find the distance between two boats. $\left(\sqrt{3}=1.732\right)$

A lift in a building of height $90$ feet with transparent glass walls is descending from the top of the building. At the top of the building, the angle of depression to a fountain in the garden is $60°$. Two minutes later, the angle of depression reduces to $30°$. If the fountain is $30\sqrt{3}$ feet from the entrance of the lift, find the speed of the lift which is descending.

An aeroplane is flying parallel to the Earth's surface at a speed of $175 \mathrm{m}/\sec$ and at a height of $600 \mathrm{m}$. The angle of elevation of the aeroplane from a point on the Earth's surface is $37°$. After what period of time does the angle of elevation increase to $53°$? $\left(\tan 53°=1.3270, \tan 37°=0.7536\right)$

A bird is flying from $A$ towards $B$ at an angle of $35°$, a point $30 \mathrm{km}$ away from $A$. At $B$ it changes its course of flight and heads towards $C$ on a bearing of $48°$ and distance $32 \mathrm{km}$ away. $C$ is $k \mathrm{km}$ to the East of $B$. Find the value of $k$.

$\left(\sin 55°=0.8192, \cos 55°=0.5736, \sin 42°=0.6691, \cos 42°=0.7431\right)$

Two ships are sailing in the sea on either side of the lighthouse. The angles of depression of two ships as observed from the top of the lighthouse are $60°$ and $45°$ respectively. If the distance between the ships is $200\left(\frac{\sqrt{3}+1}{\sqrt{3}}\right)\text{ metres}$, height of the lighthouse is $k \mathrm{metres}$. Find value of $k$.

A building and a statue are in opposite side of a street from each other $35 \mathrm{m}$ apart. From a point on the roof of building the angle of elevation of the top of the statue is $24°$ and the angle of depression of the base of the statue is $34°$. Find the height of the statue. $\left(\tan 24°=0.4452, \tan 34°=0.6745\right)$