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2 years ago

15

I think it's going to make a W, but I don't understand question 3. Can someone please explain this to me?

1 answer:

RideAnS [48]2 years ago

4 0

I thought this was a vector problem but no, this is quite easy!

You are correct; this draws the letter W.

The so-called "vector" means for you to translate the same distance. That vector goes left 3 and up 4 -- translate your point at Step 2 left 3 units and up 4 units. There you go!

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2 years ago

What is the area of the sector ?

worty [1.4K]

They forget to say "not to scale". I'm guessing this is trig because I don't see another way to do it.

Let's consider x=chord PQ first. By the Law of Cosines

$x^2 = 3^2 + 5^2 - 2(3)(5) \cos 81^\circ = 34 - 30\cos 81^\circ$

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$x^2 = 9^2 + 9^2 - 2(9)(9) \cos B$

$x^2 = 162 - 162 \cos B$

$\cos B = \dfrac{162 - x^2}{162} = 1 - \dfrac{x^2}{162}$

$\cos B = 1 - \dfrac{34 - 30\cos 81^\circ}{162}$

$B = \arccos \left(1 - \dfrac{34 - 30\cos 81^\circ }{162} \right)$

The area of the circle is the fraction given by the angle,

$A = \dfrac{B}{360^\circ} \pi r ^2$

$A \approx \dfrac{ \arccos \left(1 - \dfrac{34 - 30\cos 81^\circ}{162} \right) }{360} (3.142)9^2$

$A\approx 24.7474332960707$

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2 years ago