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zlopas [31]
3 years ago
13

HELP!!! 15 points. picture below

Mathematics
2 answers:
vlada-n [284]3 years ago
7 0

Step-by-step explanation:

\sin( \alpha )  =  \frac{ \sqrt{5} }{3}  \\  \alpha  = 48.19 \: degrees  \\   \cos( \alpha )  =  \frac{2}{3}

Vaselesa [24]3 years ago
3 0

Answer:

cos theta =± 2/3

Step-by-step explanation:

sin theta = sqrt(5) /3

sin theta = opp side / hypotenuse

We know that

a^2 + b^2 = c^2 from the pythagorean theorem

opposite side ^2 + adjacent side ^2 = hypotenuse ^2

( sqrt(5)) ^2 +   adjacent side ^2  = 3^2

5 +  adjacent side ^2  = 9

Subtract 5 from each side

5-5 +  adjacent side ^2  = 9-5

 adjacent side ^2  = 4

Taking the square root of each side

 adjacent side   = ±2

We know that

cos theta = adj side / hyp

cos theta =± 2/3

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Answer:

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Step-by-step explanation:

to find the individual angle of a REGULAR dodecagon (which means that all sides are equal), you'd use the equation I(individual angle)= (n-2)×180/n

N is number of sides. The number of sides on a dodecagon is 12. So, substitute N for 12

I= (12-2)×180/12 which simplifies to 10×180/12

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so, an individual interior angle of a dodecagon is 150°

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