# 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

Algebra ->  Algebra  -> Trigonometry-basics -> 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      Log On

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 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(6527)   (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