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Hypotenuse

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Algebra and Trigonometry

Definition

The hypotenuse is the longest side of a right triangle, opposite the right angle. It is used in various trigonometric functions such as sine and cosine.

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5 Must Know Facts For Your Next Test

  1. The Pythagorean theorem states that $a^2 + b^2 = c^2$, where $c$ is the hypotenuse.
  2. In a unit circle, the hypotenuse corresponds to the radius, which is always 1.
  3. Sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the hypotenuse: $\sin(\theta) = \frac{opposite}{hypotenuse}$.
  4. Cosine of an angle in a right triangle is defined as the ratio of the length of the adjacent side to the hypotenuse: $\cos(\theta) = \frac{adjacent}{hypotenuse}$.
  5. The hypotenuse can never be shorter than either of the other two sides in a right triangle.

Review Questions

  • What is the relationship between sine and cosine functions and the hypotenuse?
  • How does the Pythagorean theorem relate to finding the hypotenuse?
  • In a unit circle, what does the hypotenuse represent?
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