Answer: Choice D) 5.9
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We'll be using the tangent rule two times to find the lengths of BD and BC, which we'll subtract to compute the length of CD. Make sure your calculator is in degree mode.
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Focus on triangle ABC for now (ignore point D)
For reference angle A:
AB = adjacent = 85
BC = opposite = unknown = x
tan(angle) = opposite/adjacent
tan(A) = BC/AB
tan(28) = x/85
x = 85*tan(28)
x = 45.1953
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Now focus on triangle ABD (ignore point C)
For reference angle A:
AB = adjacent = 85
BD = opposite = unknown = y
tan(angle) = opposite/adjacent
tan(A) = BD/AB
tan(31) = y/85
y = 85*tan(31)
y = 51.0732
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Subtract x and y (large-small)
y-x = 51.0731-45.1953 = 5.8778
this rounds to 5.9
