A plane leaves Seattle, flies 76.0 mi at 19.0 north of east, and then changes di

Question

A plane leaves Seattle, flies 76.0 mi at 19.0 north of east, and then changes direction to 48.0 south of east. After flying at 124 mi in this new direction, the pilot must make an emergency landing on a field. The Seattle airport facility dispatches a rescue crew.

A.) In what direction should the crew fly to go directly to the field? Use components to solve this problem. Units are "degrees south of east"

B.)How far should the crew fly to go directly to the field? Use components to solve this problem. Units are "Miles"

Explanation / Answer

A) Along East direction

(76*cos(19)) + (124*cos(48)) = 154.83 mi

along north direction

(76*sin(19))-(124*sin(48)) = -67.4 mi

tan(x) = -67.4/154.83

angle is x = -23.52 degrees = 23.52 South of east

Distance is D = sqrt(67.4^2+154.83^2) = 168.86 mi

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