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Illusion [34]
3 years ago
10

MODELING WITH MATHEMATICS The fire escape forms a right triangle, as shown. Use the Pythagorean Theorem to approximate the dista

nce between the two platforms. Round your answer to the nearest tenth.
Mathematics
1 answer:
anastassius [24]3 years ago
5 0

Answer:

x = 14.13ft

Step-by-step explanation:

Given

See attachment for illustration

Required

Find x

To do this, we apply Pythagoras theorem.

From the attachment, the length of the hypotenuse is 16.7ft

While the length of the opposite/adjacent is 8.9ft

Length x is calculated using:

16.7^2 = 8.9^2 + x^2

x^2 = 16.7^2 - 8.9^2

x^2 = 199.68

Take square roots

x = \sqrt{199.68

x = 14.13ft

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\bf sin(\theta)=\cfrac{opposite}{hypotenuse}
\qquad \qquad 
% cosine
cos(\theta)=\cfrac{adjacent}{hypotenuse}
\\ \quad \\
% tangent
tan(\theta)=\cfrac{opposite}{adjacent}
\qquad \qquad 
% secant
sec(\theta)=\cfrac{hypotenuse}{adjacent}\\\\
-----------------------------\\\\
sec(\theta)=\cfrac{6}{5}\cfrac{\leftarrow hypotenuse}{\leftarrow adjacent}
\\\\\\


\bf \textit{so.. using the pythagorean theorem, we get}
\\\\\\
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\\\\\\
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but.. which is it, the positive or negative version of "b"?  well.... we know tangent is < 0, that's another way of saying, tangent is negative

now.. .tangent is opposite over adjacent... for tangent to be negative, the sign of those two must differ

so.. where does that happens? well, it happens on the 2nd and 4th quadrants, so..... which quadrant then?

well, we know the hypotenuse is always positive, is just the radius anyway, and in this case is 6
but the adjacent is positive 5, that means the adjacent is positive, thus the opposite must be negative, and that happens on the 4th quadrant

so that means \bf -\sqrt{11}=b

so... now, you have all three sides, the hypotenuse, the adjacent, and the opposite, so, just fill those in, in the ratios for cosine, sine and tangent
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Answer:

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Step-by-step explanation:

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