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The numbers 20, 99, and 101 form a Pythagorean triple. A right triangle has heights x,\(\dfrac{20}{101}\), and \(\dfrac{99}{101}\), where x is the shortest height. What is x?

 Jun 26, 2019
 #1
avatar+8724 
+4

 

sin( angle )  =  opposite / hypotenuse

 

sin( C )  =  \(\frac{20}{101}\) / \(\frac{101}{101}\)

 

sin( C  )  =  \(\frac{20}{101}\)

 

Also...

 

sin( C )  =  x / \(\frac{99}{101}\)

 

sin( C )  =  \(\frac{101}{99}x\)

 

So we can equate both expressions of  sin( C )  and solve for  x

 

\(\frac{20}{101}\ =\ \frac{101}{99}x\\~\\ \frac{20}{101}\cdot\frac{99}{101}\ =\ x\\~\\ \frac{1980}{10201}\ =\ x \)_

 Jun 26, 2019
 #2
avatar+200 
+2

Thanks, that turns out to be right Hectictar!

sudsw12  Jun 26, 2019
 #3
avatar+8724 
+3

Ok, awesome!!! smiley

hectictar  Jun 26, 2019
 #4
avatar+103122 
+2

cool cool cool

 Jun 26, 2019
edited by CPhill  Jun 26, 2019
edited by CPhill  Jun 26, 2019
 #5
avatar+23071 
+3

The numbers \(20\), \(99\), and \(101\) form a Pythagorean triple.
A right triangle has heights \(x\), \(\dfrac{20}{101}\), and \(\dfrac{99}{101}\),

where \(x\) is the shortest height.
What is \(x\)?

 

Formula:

 

\(\begin{array}{|rcll|} \hline x &=& \dfrac{\dfrac{20}{101}\cdot \dfrac{99}{101}}{\dfrac{101}{101}} \\\\ &=& \dfrac{\dfrac{20\cdot 99}{101^2}}{1} \\\\ &=& \dfrac{20\cdot 99}{101^2} \\\\ &=& \dfrac{1980}{10201} \\\\ \mathbf{x} &=& \mathbf{0.19409861778} \\ \hline \end{array}\)

 

laugh

 Jun 26, 2019

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