SOLUTION: Mike's hot-air balloon is 875.0 m directly above a highway. When he is looking west, the angle of depression to Exit 81 is 11 °. The exit numbers on this highway represent the n

Question 1159436: Mike's hot-air balloon is 875.0 m directly above a highway. When he is
looking west, the angle of depression to Exit 81 is 11 °. The exit
numbers on this highway represent the number of kilometers left
before the highway ends. What is the angle of depression, to the
nearest degree, to Exit 74 in the east?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Mike's hot-air balloon is 875.0 m directly above a highway.
When he is looking west, the angle of depression to Exit 81 is 11 °.
The exit numbers on this highway represent the number of kilometers left
before the highway ends.
What is the angle of depression, to the nearest degree, to Exit 74 in the east?
:
draw this out, the balloon, the two exits, and a point right below the balloon form two right triangles.
The distance between the exits: 81 - 74 = 7 km
The angle of depression of 11 degrees, gives an interior angle on the right triangle of 79 degrees. We can use the tangent of 79 to find the distance (a) from the 81 exit to the point right below the balloon
Since we are dealing in km, change 875m to .875 km
tan(79) =
a = 4.5 km
therefore the distance from the point below the balloon to Exit 74 is:
7 - 4.5 = 2.5 km
We can now find the tangent of the left right triangle interior angle
tan(A) =
A = 70.71 degrees
Find the angle of depression: 90 - 70.71 = 19.29 ~ 19 degrees angle of depression to exit 71
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