Properties Of Triangles - Trigonometry - Mathematics Previous Year Questions

A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 45\(^\circ\). If flies off horizontally straight way from the point O. After one second, the elevation of the bird from O is reduced to 30\(^\circ\), then the speed (in m/s) of the bird is

The height of the chimney when it is found that on walking towards it 50 m in the horizontal line through its base, the angle of elevation of its top changes from 30\(^\circ\) to 60\(^\circ\) is :

Given that a house forms a right angle view from a window of another house, and the angle of elevation from the base of the first house to the window is 60 degrees. If the separation between the two houses is 6 meters, calculate the height of the first house.

Let \(\alpha\) be the solution of \({16^{{{\sin }^2}\theta }} + {16^{{{\cos }^2}\theta }} = 10\) in \(\left( {0,{\pi \over 4}} \right)\). If the shadow of a vertical pole is \({1 \over {\sqrt 3 }}\) of its height, then the altitude of the sun is

If in a \(\Delta\)ABC, 2b² = a² + c², then \(\frac{\sin 3B}{\sin B}\) is equal to

Let \(\frac{\sin A}{\sin B}=\frac{\sin (A-C)}{\sin (C-B)}\), where \(A, B\) and \(C\) are angles of a \(\triangle A B C\). If the lengths of the sides opposite these angles are \(a, b\) and \(c\) respectively, then

The angles of a triangle are in the ratio $1: 2: 7$. The ratio of the greatest side to the least side is $(k+1):(k-1)$. The value of $k$ is

Let $A, B$ and $C$ be the angles of a triangle and $\tan \frac{A}{2}=\frac{2}{5}, \tan \frac{B}{2}=\frac{3}{7}$. Then, $\tan \frac{C}{2}$ is equal to