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2 years ago

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

28.1 feet

explaination

\cos U = \frac{\text{adjacent}}{\text{hypotenuse}}=\frac{9.6}{x}

cosU=

hypotenuse

adjacent

=

x

9.6

\cos 70=\frac{9.6}{x}

cos70=

x

9.6

x\cos 70=9.6

xcos70=9.6

Cross multiply.

\frac{x\cos 70}{\cos 70}=\frac{9.6}{\cos 70}

cos70

xcos70

=

cos70

9.6

Divide each side by cos 70.

x=\frac{9.6}{\cos 70}=28.0685\approx 28.1\text{ feet}

x=

cos70

9.6

=28.0685≈28.1 feet

Type into calculator and roundto the nearest tenth of a foot.

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Answer:

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Step-by-step explanation:

Though Process:

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what we are really concerned about is how $a$ changes as the punch is being poured into the bowl i.e $\frac{da}{dh}$

So we need another formula: Using the property of hemispheres and pythagoras theorem, we can use:

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and since we know $\frac{dh}{dt} = 1.5$

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Finally, we can put our known values:

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$h = 2cm$ from the question

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