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I need help with altitudes

 

Triangle ABC has altitudes AD, BE, and CF.  If AD = 12, BE = 18, and CF is a positive integer, then find the largest possible value of CF.

 Apr 17, 2023
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Obtuse scalene triangle.

Sides: a = 183.363   b = 122.242   c = 62.867

Area: T = 1100.179
Perimeter: p = 368.473
Semi-perimeter: s = 184.236

Angle ∠ A =163.362° = 163°21'45″ = 2.851 rad
Angle ∠ B =11.004° = 11°15″ = 0.192 rad
Angle ∠ C =5.634° = 5°38'1″ = 0.098 rad

Height: ha = 12
Height: hb = 18
Height: hc = 35 - this is the largest positive integer for the value of CF

 Apr 17, 2023

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