The correct ratio to find x is (Trigonometry)

to make life easier, ill do it:  $$\sqrt189$$  is the answer

6^2 + x^2 = 15^2. now you can solve that by yourself or on the calc

And  √189  can be simplified as = √[3^3 * 7] = √[9 * 21] =  3√21

There is something odd about the diagram.

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{72}}^\circ\right)} = {\mathtt{0.951\: \!056\: \!516\: \!295}}$$

$${\frac{{\mathtt{6}}}{{\mathtt{15}}}} = {\frac{{\mathtt{2}}}{{\mathtt{5}}}} = {\mathtt{0.4}}$$

!!!

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Yeah, Alan......I hadn't noticed that....72°  is definitely not correct.....it would mean that the shortest side would be opposite the intermediate angle....impossible.....!!!