Bidyut Guha Thakurta and Amitava Mitra Solutions for Exercise 6: Miscellaneous Exercise : Trigonometry

Sum of exterior angles of a triangle is 

If $\theta$ is an acute angle and $\sin \theta \cos \theta =\frac{1}{4}$ then, the value of $\sin \theta +\cos \theta$ is

As seen from the deck of a ship, the angle of elevations of the top and bottom of a lighthouse situated on the seaside are $60°$and $30°$. If the height of the lighthouse above the sea level is $8$ metre and the deck of the ship is at a height of $3$ metre from sea level then what is the height of the lighthouse?

From a point at a height of $30$ metre from the water level of a lake the angle of elevation of an aeroplane is $30°$ and the angle of depression of the shadow of the aeroplane in the water of the lake is $60°$. What is the height of the aeroplane from the water surface of the lake?

If $x, y$ are positive real quantity, show that the relation $\sec \theta =\frac{2xy}{(x+y{)}^2}$ is impossible.

Show that the relation${\sec }^2\theta =\frac{4xy}{(x+y{)}^2}$  is possible, only when $x=y$.

From the bottom of a 'tila' the angle of elevation of its unreachable top is $45°$. After moving $100$ metre at an angle of $30°$ along the tila the angle of
elevation becomes $60°$. Find the height of the tila in metres? $(\sqrt{3}=1732)$

From the Ferry ghat of a river $600$ metre broad two boats whose faces are opposite started to reach on the other side of the river. First boat makes an angle $30°$ with the side of the river and the second boat makes an angle $90°$ with the path of the first boat. When both the boat reach on the opposite side then what will be the distance between them?