Asked by Derek
A bee flits from flower to flower. If it leaves the hive and travels 210 m [N32°E] and then 37 m [S51°W], how far and in what direction is the bee from its hive?
Answers
Answered by
Anonymous
North= 210 cos 32 - 37 cos 51
East = 210 sin 32 - 37 sin 51
distance = sqrt (North^2 + East^2)
tan angle east of north = East/North
East = 210 sin 32 - 37 sin 51
distance = sqrt (North^2 + East^2)
tan angle east of north = East/North
Answered by
mathhelper
Using standard math-trig notation:
N32°E ----> 58°
S51°W ---> 219°
resultant = 210(cos58, sin58) + 37(cos219,sin219)
= (111.283, 178.090) + (-28.7544, -23.285)
= (82.529, 154.805)
Magnitude = √(82.283^2 + 154.805^2) = 175.43 m
for angle:
tan (angle) = 154.805/82.529 = 1.8758
angle = 61.9°
or N28.1°E in your notation.
N32°E ----> 58°
S51°W ---> 219°
resultant = 210(cos58, sin58) + 37(cos219,sin219)
= (111.283, 178.090) + (-28.7544, -23.285)
= (82.529, 154.805)
Magnitude = √(82.283^2 + 154.805^2) = 175.43 m
for angle:
tan (angle) = 154.805/82.529 = 1.8758
angle = 61.9°
or N28.1°E in your notation.
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