Prove that,a triangle can be formed using sides equal to the diagonals of any convex pentagon.

Question

A friend of mine recently gave me a problem saying,

$\textbf{Question:}$

Take any convex pentagon.Show that, we can make a triangle whose side lengths will be distinct diagonals of the pentagon.

I thought of using trigonometry but they all seemed to random.I couldn't even get started with this question.

Answer 1

Hint: Let $d$ be the longest diagonal and consider the two diagonals sharing an endpoint with $d$...