The proof here would be based on the use of the Pythagoras theorem in trigonometry.
How to prove that the length of the altitude are smaller
In a triangle getting the altitude or height will result to producing a right angled triangle. In trigonometry, a right angled triangle have the sides as the hypotenuse, the adjacent and the opposite. in this case the altitude is either the opposite or adjacent.
From Pythagoras Theorem, the hypotenuse. equals the square root of the sum of squares of the other two sides. hence is the longer side. Each leg of this triangle would be shorter than the hypotenuse. The two sides that meet at the vertex are the adjacent or the opposite and the hypotenuse.
Read more on right angle triangle here: https://brainly.com/question/1248322
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