If the angles of a triangle are in the ratio $$4:1:1$$, then the ratio of the longest side to the perimeter is

Which of the following pieces of data does NOT uniquely determine an acute-angled triangle $$ABC$$ ($$R$$ being the radius of the circumcircle)?

A man from the top of a $$100$$ metres high tower sees a car moving towards the tower at an angle of depression of $${30^ \circ }$$. After some time,the angle of depression becomes $${60^ \circ }$$. The distance (in metres) travelled by the car during this time is

A pole stands vertically inside a triangular park $$\Delta ABC$$. If the angle of elevation of the top of the pole from each corner of the park is same, then in $$\Delta ABC$$ the foot of the pole is at the