A man on the top of a tower, standing on the sea-shore, finds that a boat coming towards him takes 10 minutes for the angle of depression to change from 30⁰ to 60⁰. How soon the boat reach the sea-shore

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At  a point on the plane, the angle of elevation of the bottom of the flag staff is a and that of the top of the flag staff is β. Then the height of the tower is

From the top of a cliff 100 metre high, the angles of depression of the top and bottom of a tower are 45⁰ and 60⁰ respectively. The height of the tower is

If 2ycos θ = xsin θ and 2xsec θ - ycosec θ = 3, then the value of x² + 4y² is

A person from the top of a hill observes a vehicle moving towards him at a uniform speed. It takes 10 minutes for the angle of depression to change from 45⁰ to 60⁰.

After this the time required by the vehicle to reach the bottom of the hill is

If (a²-b²) sin θ + 2abcos θ = a²+b², then tan θ =