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BARSIC [14]
3 years ago
9

The distance between Cincinnati, Ohio, and charlotte, North Carolina, is about 336 miles.The distance between Cincinnati and Chi

cago, Illinois, is about 247 miles. If Perry drove from charlotte to Chicago by way of Cincinnati, find the distance he drove.
Mathematics
1 answer:
Sedaia [141]3 years ago
7 0
The answer will be 583 miles because from Charlotte to Cincinnati is about 336 plus, Cincinnati to Chicago is about 247 miles.
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Find the sum. then use commutative property of addition to write the related sentence
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I'll do Problem 8 to get you started

a = 4 and c = 7 are the two given sides

Use these values in the pythagorean theorem to find side b

a^2 + b^2 = c^2\\\\4^2 + b^2 = 7^2\\\\16 + b^2 = 49\\\\b^2 = 49 - 16\\\\b^2 = 33\\\\b = \sqrt{33}\\\\

With respect to reference angle A, we have:

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We'll start with the sine ratio which is opposite over hypotenuse.

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Then cosine which is adjacent over hypotenuse

\cos(\text{angle}) = \frac{\text{adjacent}}{\text{hypotenuse}}\\\\\cos(A) = \frac{b}{c}\\\\\cos(A) = \frac{\sqrt{33}}{7}\\\\

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\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(A) = \frac{a}{b}\\\\\tan(A) = \frac{4}{\sqrt{33}}\\\\\tan(A) = \frac{4\sqrt{33}}{\sqrt{33}*\sqrt{33}}\\\\\tan(A) = \frac{4\sqrt{33}}{(\sqrt{33})^2}\\\\\tan(A) = \frac{4\sqrt{33}}{33}\\\\

Rationalizing the denominator may be optional, so I would ask your teacher for clarification.

So far we've taken care of 3 trig functions. The remaining 3 are reciprocals of the ones mentioned so far.

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------------------------------------------------------

Summary:

The missing side is b = \sqrt{33}

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Rationalizing the denominator may be optional, but I would ask your teacher to be sure.

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