SOLUTION: 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 mo

Question 405670: 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.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
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.
distance=speed*time
=60km/hr*10minutes
10 minutes = 1/6 hr
distance=60*(1/6)=10km
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
(x+10)/x=15.58
15.58x=x+10
14.58x=10
x=10/14.58=.686 km
h=x tan 70
=.686 tan70=1.88km
ans: The height of the mountain is 1.88 km

RELATED QUESTIONS
Last problem I'm stuck on...please help!! A motorist, traveling along a level highway... (answered by nerdybill)

A motorist travels A to B at a speed at 40 km/h and returns at speed of 60 km/h. his... (answered by Alan3354)

A motorist made a 200 km trip averaging 50 km/h on a level road and 25 km/h on a mountain (answered by ankor@dixie-net.com)

Two bicyclists travel toward each other, each traveling at a uniform speed of 5 km/h. At... (answered by Alan3354)

A motorist traveled from Town A to Town B. After traveling 1/3 of the distance for the... (answered by TimothyLamb)

A speed trap on the highway set by the O.P.P. shows that the mean speed of cars is 103.4 (answered by ikleyn)

A motorist traveled along a straight road from Town A to Town B at 70 km/h. A... (answered by ankor@dixie-net.com)

a disabled freight train is traveling toward a station 140 km away at a speed of 32 km/h. (answered by ankor@dixie-net.com)

Two motorist undertake a journey by car. One motorist travel at an average speed of 100... (answered by ankor@dixie-net.com)