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Using the definition of tangent in a right triangle:
Question: A triangle has sides of lengths $ 13 $ cm, $ 14 $ cm, and $ 15 $ cm. What is the length of the shortest altitude?
To find the shortest altitude, we first compute the area using Herons formula.
Let the sides be $ a = 13 $, $ b = 14 $, $ c = 15 $.
The altitude corresponding to side $ a $ is: