SOLUTION: A driver in a car traveling along a straight level road at 62 miles per hour sees a mountain in the distance. The driver determines that the angle of elevation to the top of mounta

Question 1129202: A driver in a car traveling along a straight level road at 62 miles per hour sees a mountain in the distance. The driver determines that the angle of elevation to the top of mountain to be 19∘22′. After 20 minutes, the driver determines the angle of elevation to the top of the mountain to be 34∘25′. Calculate the height of the mountain to the nearest foot.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
In 20 minutes the car travels 62/3 is approximately 20.67 miles
:
22' = 22/60 is approximately 0.37 degrees
:
25' = 25/60 is approximately 0.42 degrees
:
tan 19.37 degrees = h/(x+20.67), where h is the height of the mountain, x is the horizontal distance from the mountain to the car after it has traveled 20 minutes
:
h = 0.35(x+20.67)
:
1) 0.35x +7.23 = h
:
tan 34.42 = h/x
:
2) 0.69x = h
:
solve equation 2 for x
:
x = h/0.69
:
substitute for x in equation 1
:
0.35(h/0.69) +7.23 = h
:
multiply both sides of = by 0.69
:
0.35h +4.99 = 0.69h
:
0.34h = 4.99
:
h = 4.99/0.34 is approximately 14.68 miles
:
*******************************************************************
height of the mountain is 14.68 * 5280 is approximately 77,510 feet
*******************************************************************
:
RELATED QUESTIONS
A driver moving at a constant speed sees a log in the road, but it takes time for her to... (answered by josmiceli)

fresno is 150 miles from bakersfield. A driver leaves fresno and averages 62 miles per... (answered by nerdybill)

A cyclist traveling at a constant rate of 12 miles per hour is passed by a car traveling... (answered by lwsshak3)

you are riding home from a party and the driver has been drinking. The car is traveling... (answered by vleith)

A car is traveling at 90 miles per hour when the driver applies the brakes. The cars... (answered by Alan3354)

A driver of a car is initially 550 miles from home, traveling toward home on a straight... (answered by Alan3354)

5. When the driver of a vehicle observes an obstacle in the road, the total stopping... (answered by math_tutor2020)

A van full of storm chasers is driving along a straight road at 61 miles per hour in... (answered by ankor@dixie-net.com)

A truck leaves a town traveling at 50 miles per hour. Two hours later a car leaves,... (answered by venugopalramana)