SOLUTION: Judy is driving along a highway that is climbing a steady 9-degree slope. After driving for 2 miles along this road, how much altitude has Judy gained? How far must she travel i

Algebra ->  Angles -> SOLUTION: Judy is driving along a highway that is climbing a steady 9-degree slope. After driving for 2 miles along this road, how much altitude has Judy gained? How far must she travel i      Log On


   

Question 148270: Judy is driving along a highway that is climbing a steady 9-degree slope. After driving for 2 miles along this road, how much altitude has Judy gained?
How far must she travel in order to gain a mile of altitude?
thank you very much!
Found 2 solutions by vleith, Nate:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Sin is defined as opposite/hypotenuse.
Draw a right triangle with one point at the origin. Draw the hypotenuse (h) with an angle of 9 degrees above the x axis. The "altitude" gained is given by altitude+=+h%2Asin%289%29
At 2 miles, we have altitude+=+2%2Asin%289%29 = 0.312 miles
How far must one go to be an altitude of 1 mile?
1+=+h+%2A+sin%289%29
1%2F%28sin%289%29%29+=+h+
1%2F0.1564+=+h+
6.392+miles+=+h+

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
Judy is driving along a highway that is climbing a steady 9-degree slope. After driving for 2 miles along this road, how much altitude has Judy gained?

This has to do with a leg and the hypotenuse, so tangent is ruled out. Since this involves the opposite leg and the hypotenuse, sine is required.
sin( 9* ) = x / 2
x = 0.31 miles
How far must she travel in order to gain a mile of altitude?

sin( 9* ) = 1 / x
x = 6.39 miles