# Trig

A plane is flying at 240 mph heading North 60 degrees East. The wind is blowing at South 30 degrees East at 30 mph.

What is the largest and smallest angles?

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1. Vp = 240mi/h, N60E = 30deg CCW.

Vw = 30mi/h, S30E = 300deg. CCW.

Add all hor components of velocity; and

X = hor = 240cos30 + 30cos300 =
207.8 + 15 = 222.8mi/h.

Y = ver = 240sin30 + 30sin300 =
120 - 26 = 94mi/h.

Now we have a single rt triangle with
X and Y representing the hor and ver
side, respectively.

tanA = Y/X = 94/222.8 = 0.4219,
A = 22.9deg.,CCW = N67.1E. = Bearing of
the plane.

The largest angle = 90deg.

The smallest angle = 22.9deg.,CCW.

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