A geologist stands on the shore of a lake in Ontario with a theodolite and finds that the angle of inclination to the top of a distant rock pillar is 28.5 degrees. He then walks 10 m along the shore at a 90 degree angle to his measurment, and finds that the angle to the same point on the bottom of the rock pillar is 56.4 degrees. Find the height of the rock pillar in metres, given that the theodolite was 1.6 metres above the ground.
I'm not sure I understand what angle the 56.4 degrees represents, but assuming it is the difference in horizontal azimuth to the pillar from the 1st setup to the 2nd setup then solution is:
If the distance to the pillar is "P" then:
tan(56.4)=10/P or
P=10/tan(56.4)=6.6m
if the height of the pillar is "h", then:
tan(28.5)=(h-1.6)/P