SOLUTION: An airplane is flying between two towns at an altitude of 8 km. One town is to the west of the plane at an angle of 34.1 degrees and the other is to the east of the plane at an ang

Question 1071408: An airplane is flying between two towns at an altitude of 8 km. One town is to the west of the plane at an angle of 34.1 degrees and the other is to the east of the plane at an angle of depression of 49.7 degrees. Determine the distance between the two towns, to the nearest tenth of a kilometre.
thanks
Found 2 solutions by josmiceli, KMST:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The altitude of the plane makes 2 right triangles
with vertices at
(1) the plane
(2) the towns
(3) the ground directly below the plane
----------------------------------------
The triangle to the west:
degrees at plane
Let = the distance in km from the town to the west
and the point directly below the plane
I can say:
km

----------------------
The triangle to the east:

Let = the distance in km from the town to the east
and the point directly below the plane

----------------------

The towns are 18.6 km apart
check the math

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Here is the diagram to go with josmiceli's answer:

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