Questions on Geometry: Angles, complementary, supplementary angles answered by real tutors!

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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! : 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!
Answer by vleith(1156) 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*sin(9)
At 2 miles, we have altitude = 2*sin(9) = 0.312 miles
How far must one go to be an altitude of 1 mile?
1 = h * sin(9)
1/(sin(9)) = h
1/0.1564 = h
6.392 miles = h
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! : 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!
Answer by Nate(3495) 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?
drawing( 400, 300, -10, 10, -10, 10, triangle( -8, -4, 8, -4, 8, 0 ), locate( -4, -3, 9 ), locate( 0, -0.5, 2 ), locate( 8.5, -1.5, x) )
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?
drawing( 400, 300, -10, 10, -10, 10, triangle( -8, -4, 8, -4, 8, 0 ), locate( -4, -3, 9 ), locate( 0, -0.5, x ), locate( 8.5, -1.5, 1) )
sin( 9* ) = 1 / x
x = 6.39 miles