Mathematics
A man on a cliff observes a boat, at an angle of depression 30°, which is sailing towards the shore to the point immediately beneath him. Three minutes later, the angle of depression of the boat is found to be 60°. Assuming that the boat sails at a uniform speed, determine :
(i) how much more time it will take to reach the shore ?
(ii) the speed of the boat in metre per second, if the height of the cliff is 500 m.
Related Questions
The angle of elevation of the top of a tower is observed to be 60°. At a point, 30 m vertically above the first point of observation, the elevation is found to be 45°. Find:
(i) the height of the tower,
(ii) its horizontal distance from the points of observation.
From the top of a cliff, 60 meters high, the angles of depression of the top and bottom of a tower are observed to be 30° and 60°. Find the height of the tower.
A man in a boat rowing away from a lighthouse 150 m high, takes 2 minutes to change the angle of elevation of the top of the lighthouse from 60° to 45°. Find the speed of the boat.
A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60°. When he moves 40 m away from the bank, he finds the angle of elevation to be 30°. Find :
(i) the height of the tree, correct to 2 decimal places.
(ii) the width of the river.