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2 years ago

I need help understanding how to do this.

Mathematics

1 answer:

enot [183]2 years ago

6 0

Answer:

Area of a trapezium = 1/2 * sum of parallel sides * distance between them

= 1/2 * (10 + 18) * 6

= 1/2 * 28 * 6

= 84 feet ^2

Area of a rectangle = length * breadth

= 18 * 12

= 216 feet ^2

Total Area = 84 + 216

Total area = 300 feet

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suter [353]

If you know that $\sin\dfrac\pi3=\dfrac12$ , then you know right away

$\tan\left(\sin^{-1}\dfrac12\right)=\tan\dfrac\pi3=\dfrac1{\sqrt}3=\dfrac{\sqrt3}3$

###

Otherwise, you can derive the same result. Let $\theta=\sin^{-1}\dfrac12$ , so that $\sin\theta=\dfrac12$ . $\sin^{-1}$ is bounded, so we know $-\dfrac\pi2\le\theta\le\dfrac\pi2$ . For these values of $\theta$ , we always have $\cos\theta\ge0$ .

So, recalling the Pythagorean theorem, we find

$\cos^2\theta+\sin^2\theta=1\implies\cos\theta=\sqrt{1-\sin^2\theta}=\sqrt{1-\left(\dfrac12\right)^2}=\dfrac{\sqrt3}2$

Then

$\tan\theta=\tan\left(\sin^{-1}\dfrac12\right)=\dfrac{\sin\theta}{\cos\theta}=\dfrac{\frac12}{\frac{\sqrt3}2}=\dfrac1{\sqrt3}=\dfrac{\sqrt3}3$

as expected.

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3 years ago

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umka2103 [35]

Answer:

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3 years ago

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3 years ago

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Mekhanik [1.2K]

The answer is B.

Explanation:

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