Question

A plane leaves Seattle, flies 85 mi at 22° north of east, and then changes direction to 48° south of east. After flying at 115 mi in this new direction, the pilot must make an emergency landing on a field. The Seattle airport facility dispatches a rescue crew. In what direction and how far should the crew fly to go directly to the field? Use components to solve this problem.

Answer 1

Answer:

The rescue crew should fly to go directly to the field to 164.73 mi at 18.99° south of east.

Explanation:

To know the total distance, we need to use cartesian coordinates. The distance that should fly the rescue crew to the east is the decomposition of both travels on this direction, it is the same way to the travels on the another axle. So $East = 85*Cos (22) + 115*Cos(48) = 78.81 mi + 76.95 mi = 155.76 mi$ and $South = 85*Sen (22) - 115 Sen(48) = 31.84 mi - 85.46 mi = -53.62 mi$ when we have got result of both travels, we use the trigonometric identity know Arctan; $\alpha =Arctan(\frac{-53.62}{155.76} )= -18.99(degree)$ to find the direction. Then we need to use the pythagorean theorem to get the distance that the rescue crew should travel; $R^{2}=x^{2}+y^{2} =\sqrt{155.76^{2}+(-53.62)^{2}}=164.73(mi)$. Ordering the data we get distance 164.73 mi at 18.99° south of east.