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# Geometry problem

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Guys, I'm stuck on such a task, so I've got my question to several mathematical forums and on studydaddy but I have not received an answer yet, tell me how to solve my problem?  Need urgent help!
Using the technique in the model above, find the missing sides in this 30°-60°-90°  triangle.
Long=3
Hypotenuse=??

AKM17  Mar 22, 2018
edited by AKM17  Mar 22, 2018

#1
+1873
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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
Sort:

#1
+1873
+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

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