Posted by **mikee** on Friday, January 4, 2013 at 8:54am.

An aviator heads his airplane due west. He finds that because of a wind from the south, the course makes an

angle of 20" with the heading. If his airspeed is 100 mi/h, what is his groundspeed and what is the speed of the wind?

- trigonometry math -
**Reiny**, Friday, January 4, 2013 at 9:05am
Make a sketch

His compass direction is your horizontal line with length of 100

At the end draw a vertical line upwards, (the wind direction from the south), label it y

draw in your hypotenuse h , his/hers actual course .

the angle is 20°

for speed of wind

tan 20° = y/100

y = 100tan20 = appr 36.4 mi/h

for groundspeed

cos20 = 100/h

h = 100/cos20 = appr 106.4 mi/h

check:

100^2 + 36.4^2 = 11324.96

106.4^2 = 11320.7

close enough using my rounded answer

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