In a right triangle, which of the following represents the tangent of angle θ as a ratio?

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Multiple Choice

In a right triangle, which of the following represents the tangent of angle θ as a ratio?

Explanation:
In a right triangle, the tangent of an angle is the ratio of the side opposite the angle to the side adjacent to the angle. So for angle θ, tan θ = opposite / adjacent. This makes the expression “the length of the opposite side divided by the length of the adjacent side” the correct representation. The other common ratios involve the hypotenuse (sine is opposite/hypotenuse, cosine is adjacent/hypotenuse), and the ratio of the hypotenuse to the adjacent side is cotangent, not tangent.

In a right triangle, the tangent of an angle is the ratio of the side opposite the angle to the side adjacent to the angle. So for angle θ, tan θ = opposite / adjacent. This makes the expression “the length of the opposite side divided by the length of the adjacent side” the correct representation. The other common ratios involve the hypotenuse (sine is opposite/hypotenuse, cosine is adjacent/hypotenuse), and the ratio of the hypotenuse to the adjacent side is cotangent, not tangent.

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