An ultralight plane si headed N30W at 40km/h. A 12km/h wind is blowing in the direction E20S. What is the resultant velocity of the ultralight plane with respect to the ground?
I cannot figure out how to draw the wind blowing E20S.
"In mathematics, you don't understand things. You just get used to them." -- Johann von Neumann
I would have wanted to solve the triangle using the cosine/sine law but I can not see an angle. If I go with a scale and 1cm=4km/h I get the resultant 7cm/21km/h
Any suggetions to solve it using trigonometry?
method of components ...
$\displaystyle A_x + W_x = G_x$
$\displaystyle -40\sin(30) + 12\cos(20) = G_x$
$\displaystyle A_y + W_y = G_y$
$\displaystyle 40\cos(30) - 12\sin(20) = G_y$
$\displaystyle |G| = \sqrt{(G_x)^2 + (G_y)^2}$
$\displaystyle \theta = \arctan\left(\frac{G_y}{G_x}\right) + 180$
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And you can still use geometry:
Put another direction at the upper tip of the triangle. From parallel lines, you know that the lower angle is 30 degrees. And since those angles are found in a right angle, you can deduce that the middle angle is 90 - (30 + 20) = 40 degrees.
From there, you can use the cosine rule and the sine rule to get angle x, which you use to determine the resultant angle.