Question

In the figure, the rectangular plane ABCD is a hillside with inclination 30. C' and O' are vertically below C and O respectively so that A,B,C',O' are on the hillside which makes an angle 60 with BC, and OT is a vertical tower. AB=2000m, BO=1000m and OT=50m.
(a) Find BC and CC'.
(b) Find the inclination of BO with the horizontal.
(c) Find AT.
(d) There are cable cars going directly from A to T. A man want to go to T from B and he can do this by taking either one of the following routes:
Route I: Walking uphill along BO at an average speed of 0.3 m/s and taking a lift in the tower for 1 minute from O to T.
Route II: Walking along BA at an average speed of 0.8 m/s and taking a cable car from A to T at an average speed of 3.2 m/s.
Determine which route takes a shorter time.