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If the hypotenuse of a right triangle is 2sqrt(3) units long and one of the legs is sqrt(3) units long, then how long is the other leg?

 Feb 21, 2019
edited by travisio  Feb 21, 2019
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There is a quick answer to this.....but let's solve it algebraically, first

 

Note   2sqrt(3) =  sqrt(12)

 

So.....the remaining leg is

 

√ [ [sqrt(12)]^2 - [sqrt (3)]^2 ]    =  √ [12 - 3] = sqrt [ 9 ] =    3 units

 

 

Note that if the hypotenuse is  2√3     and   the shortest leg  is  √3......then we have a 30 -60 -90 right triangle

 

The the angle opposite the hypotenuse =  90°

The angle opposite the shortest leg = 30°

 

So.....the remaining leg is opposite the 60°   =    √3 *√3    =     3     ...just what we  found !!!!

 

 

 

 

 

cool  cool cool

 Feb 21, 2019

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