ShmoopTube

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For a good time, solve this shmoopy question.

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If the cosine X equals root 2 over 2 ,what is the measure of angle x?

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And here are the choices.

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Okay, we know that cosine measures the adjacent side

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over the hypotenuse. So we can figure out the triangle look something like this.

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First we should find out length of the final side

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by using the Pythagorean Theorem - A sqaured plus B squared equals C squared

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we can determine that root 2 squared plus

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X squared equals 2 squared. That's 2 plus x squared equals 4...

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Subtract 2 from both sides and X squared equals 2.

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Take the square root of both sides and X equals the square root of 2.

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Awesome. That means we have an isosceles triangle where two sides are equal

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better yet when two sides are equal that means that 2

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angles are equal. Even better we already know that one angle is 90 degrees

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since the triangle is a right triangle, which means

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that the other two angles have to measure 45 degrees each

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and we have our answer it's C.

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