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D. 5.9
Math Question No Guessing Please help

D. 5.9 Math Question No Guessing Please help-example-1
User Granth
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2 Answers

1 vote

We will make use of our trigonometric functions in this problem.



\tan(31^(\circ)) = \frac{\overline{DB}}{\overline{AB}}


\tan{31^(\circ)} = \frac{\overline{DB}}{85}


85 \cdot \tan({31^(\circ)}) = \overline{DB}


Now that we know
\overline{DB} we need to find
\overline{CB}, since
\overline{CD} = \overline{DB} - \overline{CB}.


\tan(28^(\circ)) = \frac{\overline{CB}}{\overline{AB}}


\tan(28^(\circ)) = \frac{\overline{CB}}{85}


85 \cdot \tan(28^(\circ)) = \overline{CB}


Therefore, we can come to our final answer:


\overline{CD} = \boxed{85\tan(31^(\circ)) - 85\tan(28^(\circ))} \approx \boxed{5.88}

User Subby
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3 votes

So for this, we will be using tangent (tan = opposite/adjacent) to solve for the sides BD and BC, then subtract the two sides to get CD.

Triangle ABC has ∠A = 28 degrees. Since we have the adjacent side (AB = 85) and we need to solve for the opposite side, we are using tangent. Our equation will look as such:
(tan(28))/(1) =(BC)/(85)

For this, just cross-multiply and your answer will be (Rounded to the tenths):
BC=45.2

Next, Its the same process with triangle ABD as ABC except that the angle is 31 degrees instead of 28.


(tan(31))/(1) =(BD)/(85)\\ \\ BD=51.1

Next, subtract the two sides together and your answer will be 5.9, or D.

User Hodgef
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8.1k points

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