ShmoopTube

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Here's your shmoop du jour

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If tan(x) = square root of 3, what is the measure of the angle?

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And here are the potential answers...

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It's asking us to find x, or the measure of the angle that makes the tangent of x equal

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to root 3.

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Remember your triangle trig ratios?

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Tangent is opposite over adjacent.

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The ratio of the opposite side of the angle x over the adjacent side to x is the square root of

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3 or root 3 over 1. Okay. Pythagorean Theorem time!

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squared.

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One squared plus root three squared equals the hypotenuse squared. One plus three equals

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the hypotenuse squared... so four equals the hypotenuse squared.

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Take the square root of both sides, and we get that the hypotenuse equals 2.

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The ratio of the sides is 1 to √3 to 2, which means this is a special triangle.

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It's a 30-60-90 triangle, and x, the angle opposite the second longest side is the second

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largest angle, which makes it 60 degrees. Option D is the correct answer.

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