posted by Winsel on .
An observer at A looks due north and sees a meteor with an angle of elevation of 70deg. At the same instant, another observer 30miles east of A, sees the same meteor and apprroximates its position as N 50deg W but fails to note its angle of elevation. Find the height of the meteor and its distance form A.
The line of sight of the 2nd observer
is represented by the hypotenuse of a rt triangle, and the height of the
meteor is represented by the ver. side
of the rt triangle.The acute angle bet.
ween the ver. side and hyp. = 50 deg.
The angle of elevation is equal to the
other acute angle or 40 deg.
Tan(40) = h/30,
h =30*Tan(40) = 25.2 =height of
Tan(70) = 25.2 / d,
d = 25.2/Tan(70) = 9.2 = distance of
Sin(70) = 25.2/d,
d = 25.2/Sin(70) =26.8.