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Using the technique in the model above, find the missing sides in this 30°-60°-90° triangle.

Long=3

Hypotenuse=??

AKM17
Mar 22, 2018

#1**+1 **

A 30-60-90 triangle is a special type of right triangle where the ratio of the sides are already known. The sides have a constant ratio of \(1:\sqrt{3}:2\). Using this information, it is possible to find the hypotenuse by setting up a proportion.

\(\frac{\text{long}}{\sqrt{3}}=\frac{\text{hypotenuse}}{2}\)

Of course, we already know the length of the "long" side, so it is possible to solve for the length of the hypotenuse.

\(\frac{\text{long}}{\sqrt{3}}=\frac{\text{hypotenuse}}{2}\) | Replace "long" with 3 since that is its side length. |

\(\frac{3}{\sqrt{3}}=\frac{\text{hypotenuse}}{2}\) | Multiply by 2 on both sides to get rid of the fraction on the right hand side. |

\(\text{hypotenuse}=\frac{6}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}}\) | Multiplying by the square root of 3 like this will rationalize the denominator. |

\(\text{hypotenuse}=\frac{6\sqrt{3}}{3}=2\sqrt{3}\approx 3.464\) | The decimal approximation seems reasonable because it should be the longest side of the triangle. |

TheXSquaredFactor
Mar 22, 2018

#1**+1 **

Best Answer

A 30-60-90 triangle is a special type of right triangle where the ratio of the sides are already known. The sides have a constant ratio of \(1:\sqrt{3}:2\). Using this information, it is possible to find the hypotenuse by setting up a proportion.

\(\frac{\text{long}}{\sqrt{3}}=\frac{\text{hypotenuse}}{2}\)

Of course, we already know the length of the "long" side, so it is possible to solve for the length of the hypotenuse.

\(\frac{\text{long}}{\sqrt{3}}=\frac{\text{hypotenuse}}{2}\) | Replace "long" with 3 since that is its side length. |

\(\frac{3}{\sqrt{3}}=\frac{\text{hypotenuse}}{2}\) | Multiply by 2 on both sides to get rid of the fraction on the right hand side. |

\(\text{hypotenuse}=\frac{6}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}}\) | Multiplying by the square root of 3 like this will rationalize the denominator. |

\(\text{hypotenuse}=\frac{6\sqrt{3}}{3}=2\sqrt{3}\approx 3.464\) | The decimal approximation seems reasonable because it should be the longest side of the triangle. |

TheXSquaredFactor
Mar 22, 2018