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on a map the town of morgan run is due south of davidson and is southeast of vicksburg. the distance from morgan run to davidson and vicksburg is 32 and 52 miles respectively. the distance between davidson and vicksburg is 42 miles. if a place leaves morgan to fly to vvick what bearing should it travel
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Let θ be the angle between north (the line MD) and the line MV. In triangle MDV (with MD = 32, MV = 52, DV = 42) use the law of cosines at M:
cos θ = (MD^2 + MV^2 − DV^2) / (2·MD·MV)
= (32^2 + 52^2 − 42^2) / (2·32·52)
= 1964 / 3328 = 491/832 ≈ 0.590625.
θ = arccos(0.590625) ≈ 53.84°.
Because Vicksburg is west of Morgan Run, the bearing from Morgan Run to Vicksburg is N 53.84° W, which is equivalent to a compass bearing of about 306.16° (≈ N 53°50' W).
cos θ = (MD^2 + MV^2 − DV^2) / (2·MD·MV)
= (32^2 + 52^2 − 42^2) / (2·32·52)
= 1964 / 3328 = 491/832 ≈ 0.590625.
θ = arccos(0.590625) ≈ 53.84°.
Because Vicksburg is west of Morgan Run, the bearing from Morgan Run to Vicksburg is N 53.84° W, which is equivalent to a compass bearing of about 306.16° (≈ N 53°50' W).
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