If in $\triangle ABC$ $\angle A + \angle B = 90^\circ$ and $\sin B = \frac{4}{5}$, then find the value of $\cos A$.

From a point P on the ground the angle of elevation of the top of 10 m high building is $30°$. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from the point P is $45°$. Length of the flagstaff is:

(Take $\sqrt{3} = 1.732$)

A tower is 50 m high. The angle of elevation of the top of the tower from a point on the ground is 30°. Find the distance of the point from the base of the tower.

The tops of two poles of height 22 m and 31 m are connected by a wire. If the wire makes an angle of 60° with the horizontal, then the length of the wire (in m) is:

If the angles of elevations of the top of a tower from two points at distances a and b from the base and in the same straight line with it are complementary then the height of the tower is

If $3\sin\theta - 4\cos\theta = 0$, then value of $\tan\theta\cdot\csc\theta$ is :

Find the angle of elevation of the Sun, when the length of the shadow of a tree is $\frac{1}{\sqrt{3}}$ times the height of the tree.