hypotenuse

Examples of hypotenuse in the following topics:

• Arc Length and Speed

  • By the Pythagorean Theorem, each hypotenuse will have length $\sqrt{dx^2 + dy^2}$.
  • Adding up each tiny hypotenuse yields the arc length.
  • where the rate of change of the hypotenuse length depends on the rate of change of $x$ and $y$.
  • The length of a curve can be approximated by using a series of right triangles with the hypotenuses lying along the curve.

• Trigonometric Functions

  • The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.
  • In our case $\sin A = \frac {\textrm{opposite}} {\textrm{hypotenuse}} = \frac {a} {h}$ .
  • The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse: so called because it is the sine of the complementary or co-angle.
  • In our case $\cos A = \frac {\textrm{adjacent}} {\textrm{hypotenuse}} = \frac {b} {h}$.