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anzhelika [568]
2 years ago
14

In ΔTUV, the measure of ∠V=90°, the measure of ∠U=70°, and UV = 9.6 feet. Find the length of TU to the nearest tenth of a foot.

Mathematics
1 answer:
Nutka1998 [239]2 years ago
8 0

​

<u><em>28.1 feet</em></u>

<u><em></em></u>

<em><u>explaination</u></em>

<u><em>\cos U = \frac{\text{adjacent}}{\text{hypotenuse}}=\frac{9.6}{x}</em></u>

<u><em>cosU= </em></u>

<u><em>hypotenuse</em></u>

<u><em>adjacent</em></u>

<u><em>​ </em></u>

<u><em> = </em></u>

<u><em>x</em></u>

<u><em>9.6</em></u>

<u><em>​ </em></u>

<u><em> </em></u>

<u><em>\cos 70=\frac{9.6}{x}</em></u>

<u><em>cos70= </em></u>

<u><em>x</em></u>

<u><em>9.6</em></u>

<u><em>​ </em></u>

<u><em> </em></u>

<u><em>x\cos 70=9.6</em></u>

<u><em>xcos70=9.6</em></u>

<u><em>Cross multiply.</em></u>

<u><em>\frac{x\cos 70}{\cos 70}=\frac{9.6}{\cos 70}</em></u>

<u><em>cos70</em></u>

<u><em>xcos70</em></u>

<u><em>​ </em></u>

<u><em> = </em></u>

<u><em>cos70</em></u>

<u><em>9.6</em></u>

<u><em>​ </em></u>

<u><em> </em></u>

<u><em>Divide each side by cos 70.</em></u>

<u><em>x=\frac{9.6}{\cos 70}=28.0685\approx 28.1\text{ feet}</em></u>

<u><em>x= </em></u>

<u><em>cos70</em></u>

<u><em>9.6</em></u>

<u><em>​ </em></u>

<u><em> =28.0685≈28.1 feet</em></u>

<u><em>Type into calculator and roundto the nearest tenth of a foot.</em></u>

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Step-by-step explanation:

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Option C:

f(x) = 5x + 7 is the function of the input-output table.

Solution:

Option A: f(x) = 6x + 9

Input x = 1 in the above equation.

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Option B: f(x) = 7x + 5

Input x = 1 in the above equation.

f(1) = 7(1) + 5

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Input x = 5 in the above equation.

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But the output is 32 in the table.

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Option C: f(x) = 5x + 7

Input x = 1 in the above equation.

f(1) = 5(1) + 7

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Input x = 5 in the above equation.

f(5) = 5(5) + 7

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Input x = 10 in the above equation.

f(10) = 5(10) + 7

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All outputs are correct for the given input.

Hence it is the function of the table.

Option D: f(x) = 12x + 1

Input x = 1 in the above equation.

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Input x = 5 in the above equation.

f(5) = 12(5) + 1

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But the output is 32 in the table.

So, it is not the function of the table.

Hence Option C is the correct answer.

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