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In triangle $ABC,$ $AB = 10,$ $BC = 24,$ and $AC = 26.$ Find the length of the shortest altitude in this triangle.

 Jul 16, 2021
 #1
avatar+805 
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If you know trig: bash each angle 

if you don't: note that it is a Pythagorean triple and you coil dddfine var for the st[hottest length, set eq and solve

 Jul 16, 2021
 #2
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Shortest altitude = (10 * 24) / 26

 Jul 16, 2021
 #3
avatar+121065 
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We  have  a right triangle  with    legs AB  and BC   and  hypotenuse  AC

 

The area  of  this triangle =   (1/2)(10) (24)  =  120

 

The  shortest altitude   is  drawn  from the  vertex opposite  the  longest side  to the longest side ( B  to AC )

 

This  altitude  can be  found as

 

Area  = (1/2) ( AC)  (altitude)

 

120  =  (1/2) (26) ( altitude )

 

120  =  13    (altitude)

 

120  / 13   =  altitude

 

cool cool cool

 Jul 16, 2021

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