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3 years ago

12

How many degrees are in EACH angle of a REGULAR 8-sided polygon? (Hint - Do the triangle trick) (Hint - Remember your definition

of a regular polygon)

1 answer:

marishachu [46]3 years ago

6 0

Answer:

135

Step-by-step explanation:

interior angles sum=(n-2)x180

8 interior angles

(8-2)x180=1080

1080/8=135

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Which Greek geometer founded a philosophical society that devoted itself to the study of mathematics

nexus9112 [7]

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3 years ago

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To avoid dehydration, a person should drink 8 ounces of water for every 15 minutes of exercise. How much water should Hahn drink

Lostsunrise [7]

Answer:

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Step-by-step explanation:

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3 years ago

I don't need you to work it out, just theorem(s) i need to reach the answer :)

VikaD [51]

Not sure why such an old question is showing up on my feed...

Anyway, let $x=\tan^{-1}\dfrac43$ and $y=\sin^{-1}\dfrac35$ . Then we want to find the exact value of $\cos(x-y)$ .

Use the angle difference identity:

$\cos(x-y)=\cos x\cos y+\sin x\sin y$

and right away we find $\sin y=\dfrac35$ . By the Pythagorean theorem, we also find $\cos y=\dfrac45$ . (Actually, this could potentially be negative, but let's assume all angles are in the first quadrant for convenience.)

Meanwhile, if $\tan x=\dfrac43$ , then (by Pythagorean theorem) $\sec x=\dfrac53$ , so $\cos x=\dfrac35$ . And from this, $\sin x=\dfrac45$ .

So,

$\cos\left(\tan^{-1}\dfrac43-\sin^{-1}\dfrac35\right)=\dfrac35\cdot\dfrac45+\dfrac45\cdot\dfrac35=\dfrac{24}{25}$

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3 years ago