Question

Question 5 (25 marks) a) A hot air balloon is hovering 800m directly above a lake. The balloon is observed by the crew of a boat as they look upwards at an angle of 20. Four minutes later, the crew has to look at an angle of 65° to see the hot air balloon. How fast was the boat traveling in meters per minute? b) Given the triangle ABC, IABI 15, IACI 12 and BAC 60°. Find IBCI. (6) c) Sketch the graph for 2cos(x) and cos(2x) between 0 and 2T. d) Solve the equation cos (4x) = 0, where 0 x

Answer 1

Let Ballon at point D, at height of 800 m above the river (Lake) when crew at point A then angle is 20 degree After 4 minute crew reached at point B and now angle is 65 degree Let crew travelled x m in 4 minute to reach point B from A Let Ac = d Therefore BC = -d - x In triangle BCD, tan 65 = DC/BC = > tan 65 = 800/d - x d - x = 800/tan 65 x = d - 800/tan 65 degree 1 In triangle ACD, tan 20 = 800/d = > d = 800/tan 20 Put value of 'd' in 1, we get, x = (800/tan 20 - 800/tan 65) = 800 (1/tan 20 - 1/tan 65) = 800 (2.7475 - 0.4663) tan 20 = 0.36397 tan 65 = 2.14451 = 800 times 2.2844 x = 1827.52 m \r\n This is the distance travelled in 4 minutes Therefore speed of boat = Distance Travelled/Time taken = 1827.52/4 meter per minute