WEBVTT

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For an acute angle theta in a right triangle, each trig function is a ratio of two sides.

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Sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent.

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Here the side opposite theta is five and the hypotenuse is thirteen.

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By the Pythagorean theorem, the adjacent side is the square root of one hundred sixty nine minus twenty five, which is twelve.

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Sine theta is five thirteenths.

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Cosine theta is twelve thirteenths.

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Tangent theta is five twelfths.

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To recap: label the sides relative to the angle, find any missing side, and check that tangent equals sine divided by cosine.