David B.
asked • 11/16/19Find the distance of the plane from point A and the elevation of the plane.
A pilot is flying over a straight highway. He determines the angles of the depression to two mileposts, 2.3 km apart, to be 26 degrees and 49 degrees. Find the distance of the plane from point A and the elevation of the plane. (I would appreciate it if someone could show me how to do this step by step)
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1 Expert Answer
Sam Z. answered • 11/16/19
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4.3
(12)
Math/Science Tutor
b=4.6
α=26°
β=49°
rt triangle=
I'm getting mixed-up. Please show a diagram.
A 26° angle of depression?
Sam Z.
I'm trying again: I take it the depression is 26deg(beta) down; then 49deg is an extra 23deg. So side "b"=2.3km; and (alpha)=23. You want side "a". To start with a/sin(alpha)=b/sin(beta)=c/sine(gamma). b/sin(beta)=2.3/26sin=5.246=a/sin(alpha). a=2.047. a^2+b^2=c^2=2.05^2+2.3^2 so c=3.081. Point a is side "b" of the oblique triangle. To get height the oblique triangle will get a rt triangle drawn from "gamma" horizontal; rt angle up to (beta). gamma is now 90deg; c=2.05; alpha=41deg because 23+26+41=90. Side "b" is the height. b/sin(beta)=b/sin49=2.05 which is side "c" (on this rt triangle) so b=1.547km.
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11/16/19
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Mark M.
Where is point A located?11/16/19