Help with precalculus homework!?

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1 Answer
Dean R.
May 1, 2018

# d = 135 sqrt{2 - 2 cos 6^circ} approx 14.1 # choice (C).

Explanation:

If instead of going along the x axis, you went at six degrees, after 135 miles instead of being at (135,0) you'd be at (135 cos 6^circ , 135 sin 6^circ). The distance #d# between those satisfies

# d^2 = (135-135 cos 6^circ)^2 + (135 sin 6^circ)^2 #

#d^2 = 135^2 ( (1 - cos 6^circ)^2 + sin^2 6^circ ) #

#d ^2 = 135 ^2 (1 - 2 cos 6^circ + cos ^2 6 + sin ^2 6) #

# d^2 = 135^2 (2 - 2 cos 6^circ) #

# d = 135 sqrt{2(1 - cos 6^circ) } #

# d approx 14.1 #

Choice [C]

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