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Triangle Lengths and Ratios: Opposite and Hypotenuse Relationship

Learn how to find lengths in a triangle using the opposite and hypotenuse sides and the sine ratio. Label the triangle, substitute values, and rearrange formulas to solve for lengths.

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Triangle Lengths and Ratios: Opposite and Hypotenuse Relationship

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  1. This is opposite the angle. There are three ratios that you need to learn: This is opposite the right-angle hypotenuse opposite adjacent This is next to the angle Remember Where are the hypotenuse, adjacent and opposite lengths.

  2. Finding a length You need to label all the lengths of the triangle. hypotenuse 10cm The adjacent is not needed in this question; the question is only using opposite and hypotenuse. opposite adjacent

  3. Finding a length You need to label all the lengths of the triangle. hypotenuse 10cm The adjacent is not needed in this question; the question is only using opposite and hypotenuse. opposite

  4. Finding a length We need to use the sine ratioand substitute the values/variables that we know. hypotenuse 10cm opposite

  5. Finding a length We need to solve the equation (*). hypotenuse 10cm opposite We can think of this as: OR rearrange the equation (*) by multiplying both sides by x.

  6. These two triangles are very different. The variable x will be on the denominator This is an example of where we have to solve an equation with the variable on the denominator, so multiply both sides by x. still need to get x on its own, so divide both sides by sin30

  7. 2. Pick the correct formula 1. label the triangle 15cm opposite 3. Substitute in the correct values adjacent 4. Rearrange to find x

  8. 15cm opposite adjacent

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