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an observer spots 2 planes directly overhead. the angle of elevation from the runway to the planes is 18* and 25*. if the two planes are 300m apart, directly above eachother, calculate the distance from the observer to the runway.

2007-06-09 20:13:36 · 2 answers · asked by Anonymous in Science & Mathematics Mathematics

2 answers

Call the distance from observer to runway D and the height of the lower plane h. This yields two equations using tangent:

tan 18 = h/D
tan 25 = (h+300)/D

If you divide equation 1 by equation 2, you get:

tan18/tan25 = h/(h+300)
.6968(h+300) = h
.6968 + 209.04= h
h = 689.4215571m

Therefore, D = h/tan18 = 2121.8m

2007-06-10 05:18:16 · answer #1 · answered by Kathleen K 7 · 0 0

y + 300 = dtan25
y = dtan18
(y + 300)/y = tan25/tan18
y + 300 = ytan25/tan18
y(tan25/tan18 - 1) = 300
y = 300/(tan25/tan18 - 1)
d = 300/(tan18)(tan25/tan18 - 1))
d = 2,121.8 m

2007-06-09 20:29:42 · answer #2 · answered by Helmut 7 · 0 0

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