A surveyor measures the angle of elevation of the top of the mountain from a point (P) at sea level as 30 detre along a track which slopes uniformly uphill towards the mountain. From this point, which is 50 metre above sea level, he measures the angle of elevation as 40 degree. (a) Find the value of x. (b) If PA = d m and AT = h m, express d in terms of h. (c) If AB = y m, express y in terms of h. (d) Find the height of the mountain above sea level, correct to the nearest meter.

Question

A surveyor measures the angle of elevation of the top of the mountain from a point (P) at sea level as 30 detre along a track which slopes uniformly uphill towards the mountain. From this point, which is 50 metre above sea level, he measures the angle of elevation as 40 degree.                           (a) Find the value of x.                                                   (b) If PA = d m and AT = h m, express d in terms of h. (c) If AB = y m, express y in terms of h.             (d) Find the height of the mountain above sea level, correct to the nearest meter.