1.A countour map with scale of 1: 100000. The differences in height between every two consecutive contour lines are the same. the height of each contour line is not indicated, but a person knows from a sign of the road that the gradient of AB is 1 in 10. (AB= 1 and BC= 1.5 are measures on the map before.) Find the angle of inclination of BC.( coorect to 1 decimal place.)
2.Steven used the following method to find the height of the tower CD. He firstly moved to point A in front of the tower where the angle of elevation measured 45(degree) from point A to the top of the tower. He then moved 50m backward to point B where the angle of elevation to the top of the tower became 30 (degree). It is given that BAD is a straight line on the horizontal level. Find the height of the tower.
3. A submarine sails near an unmoving warship. It is given that submarine is 300m down the sea-level ans sails at a constant speed. If the angle of depression from the warship to the submarine is 8.5(degree) nowand 16.7(degree) two minutes later, find the speed of the submarine. (nearest 0.1 km/h)
4.From the deck of a boat, the angle of elevation of a helicopter is 53(degree). From the top of a mast which is 10m above the deck, the angle of elevation of the helicopter is 44(degree). How high is the helicopter from the deck?
5. From half-way up a lighthouse, the angle of depression of a boat is 23(degree). What wil the angle of depression be of the same boat from the top of the lighthouse?