Right-triangle ratios

What this lesson shows

Same triangle — 3, 4, 5. But now stand at this corner: the angle called theta. From where theta sits, every side of the triangle gets a name.

Try it yourself

Real questions from this lesson's worksheets — answers below each one.

1. Right triangle: opposite = 3, hypotenuse = 5. Find sin θ
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   3/5
2. Faye writes sin θ = adjacent/hypotenuse. What's wrong?
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   sin uses the OPPOSITE side: sin θ = opposite/hypotenuse
3. In a right triangle with opposite 3, adjacent 4, hypotenuse 5, which ratio equals 3/5?
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   sin θ
4. A ramp rises 3 m over a horizontal base of 4 m. Find tan θ for the ramp's angle
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   3/4