SOLUTION: Hi appreciated math tutors, I just cannot figure this problem out...please help! A car is traveling on a level road toward a mountain two Km high. The angle of elevation from the

Algebra ->  Trigonometry-basics -> SOLUTION: Hi appreciated math tutors, I just cannot figure this problem out...please help! A car is traveling on a level road toward a mountain two Km high. The angle of elevation from the      Log On


   

Question 1080630: Hi appreciated math tutors,
I just cannot figure this problem out...please help!
A car is traveling on a level road toward a mountain two Km high. The angle of elevation from the car to the top of the mountain changes from 6 deg. to 15 deg. How far has the car traveled?
Please give me a clear example of how to work this out. Thank You!!
Found 3 solutions by rapture, josgarithmetic, ikleyn:
Answer by rapture(86) About Me  (Show Source):
You can put this solution on YOUR website!

tan(6°) = 2/(x + d)
tan(15°) = d/2

Above you have two trigonometric equations in two unknowns, d and x. Solve it as an algebra system of equations from algebra 2. Take it from here. Good luck!

Answer by josgarithmetic(39629) About Me  (Show Source):
You can put this solution on YOUR website!
Two right triangles each with vertical leg, height, 2 km. Difference between horizontal legs is what question means.

2%2Ftan%286%29-2%2Ftan%2815%29

Answer by ikleyn(52874) About Me  (Show Source):
You can put this solution on YOUR website!
.
The setup by "rapture" is incorrect.

The correct setup is this

tan(6°) = 2/(x + d)
tan(15°) = 2/d,

where d and x are distances in kilometers.

It implies

x = 2%2Ftan%286%5Eo%29 - 2%2Ftan%2815%5E0%29.