Answer:
[tex]\large\boxed{z=\dfrac{15\sqrt3}{2}[/tex]
Step-by-step explanation:
Lookat the picture.
We have
[tex]2a=15\to a=\dfrac{15}{2}\to a\sqrt3=\dfrac{15\sqrt3}{2}[/tex]
small triangle:
[tex]x=2a=\dfrac{15}{2}\to a=\dfrac{15}{4}\to y=\dfrac{15\sqrt3}{4}[/tex]
[tex]a+b=15\to b=15-\dfrac{15}{4}=\dfrac{60}{4}-\dfrac{15}{4}=\dfrac{45}{4}[/tex]
[tex]a=\dfrac{15}{4}\\\\b=\dfrac{45}{4}\\\\x=\dfrac{15}{2}\\\\y=\dfrac{15\sqrt3}{4}\\\\z=\dfrac{15\sqrt3}{2}[/tex]
