Two sides of a triangle are a and b. Find the angle between them such that area shall be maximum

Two sides of a triangle are x and y. Find the angle between them such that area shall be maximum.

Two angles of a triangle are 30^@ and 80^@ . Find the third angle.

The two adjacent sides of a cyclic quadrilateral are 2a n d5 and the angle between them is 60^0dot If the area of the quadrilateral is 4sqrt(3) , find the remaining two sides.

If two adjacent sides of a cyclic quadrilateral aré 2 and 5 and the angle between them is 60°. If the third side is 3, then the remaining fourth side is (a) 2 (b) 3 (c) 4 (d) 5

If A and B are the two points. Find the distance between them : .

Two sides of a triangle are of lengths sqrt6 and 4 and the angle opposite to smaller side is 30^@ . How many such triangles are possible ? Find the length of their third side and area.

The sides of a quadrilateral are 5 cm,12 cm, 14 cm and 15 cm and the angle between the first two sides is a right-angle. Find its area.