The speed of an airplane is 275 mi/h relative to the air. The wind is blowing due north with a speed of 25 mi/h. In what direction should the airplane head in order to arrive at a point due west of its location?

Step-by-step explanation:

The free-body diagram of the information given in the question is attached in the image below.

Using the property of Vector Right Triangle:

cos θ = adjacent/hypotenuse

cos θ = 25 mi/h / 275 mi/h

cos θ = 0.0909

θ = cos⁻¹ (0.0909)

θ = 84.79°

Therefore,  the airplane should head in the direction of S 84.79° W to reach the desired location.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4