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Worth 25 help and show work :)

Worth 25 help and show work :)-example-1
User Tanzmaus
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1 Answer

3 votes

Answers:

x = 7*sqrt(3)

y = 7

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Step-by-step explanation:

We have a 30-60-90 triangle here since the missing acute angle is 90-60 = 30 degrees. Or you could note how 30+60+90 = 180.

The side length y is the shorter leg as it's opposite the smallest angle. It's equal to half of the hypotenuse. So y = 14/2 = 7.

The longer leg x is equal to y*sqrt(3). We multiply the shorter leg by sqrt(3) to get the longer leg. This means

x = y*sqrt(3) = 7*sqrt(3)

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You could also use the pythagorean theorem if you knew that y = 7 and you had the hypotenuse value as well. You could solve like so

a^2 + b^2 = c^2

7^2 + b^2 = 14^2

b^2 = 14^2 - 7^2

b^2 = 147

b = sqrt(147)

b = sqrt(49*3)

b = sqrt(49)*sqrt(3)

b = 7*sqrt(3)

Which matches up with the value of x we found earlier.

User SarangArd
by
3.7k points