An observer (O) spots a bird flying at a 35 degrees angle from a line drawn horizontal to its nest. If the distance from the observer (O) to the bird (B) is 21,000 ft., how far is the bird (B) from its nest (N)?

1 Answer
Hammer
Feb 20, 2018

#21000/sin(35°)#

Explanation:

Assuming that the angle BON is a right angle, and that the measure of the angle BNO is 35°, then :
#sin("BNO") = "opposite"/"hypotenuse"#
#sin(35°) = "OB"/"BN"#

#sin(35°)/"OB" = 1/"BN"#

#21000/sin(35°) = "BN"#

#"BN" = 21000/sin(35°) "ft"#

#sin(35°)# is approximately #0.57#, so when used in the formula, it gives that

#"BN" = 36842.1 "ft"#.

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