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A motorist, traveling along a level highway at a speed of 60 km/h directly toward a mountain, observes that between 1:00 PM and 1:10 PM, the angle of elevation to the top of the mountain changes from 10 degrees to 70 degrees. Approximate the height of the mountain.
First, let us find out the distance the motorist traveled between 1:00 and 1:10,travel time of 10 minutes.
10 minutes = 1/6 hr
Call this distance, d=10km
Call the height of the mountain,h
Call x, the distance the motorist would have traveled after 1:10 to reach the mountain.
At 1:00 position
tan 10 deg=h/(x+d)
h=(x+d)tan 10 deg
=(x+10) tan 10 deg
At 1:10 position
tan 70 deg=h/x
h=(x)tan 70 deg
equating the two equations,
(x+10) tan 10 deg=(x)tan 70 deg
(x+10)/x=(tan 70 deg)/(tan 10 deg)=15.58
h=x tan 70
ans: The height of the mountain is 1.88 km