trigonometry math
posted by mikee on .
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?

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