Answer:
The answer is [tex]a = \frac{15}{4}[/tex]
Step-by-step explanation:
We have to:
[tex]cos(\theta) = \frac{adjacent\ side}{hypotenuse}[/tex]
So, if we take the 60 degree angle of the smallest triangle, we have to:
[tex]cos(60) = \frac{a}{x}[/tex]
We do not know x. But if we take the sine of the angle of 30 degrees and the main triangle we have:
[tex]sin(30) = \frac{x}{15}\\\\x =\frac{15}{2}[/tex]
Then:
[tex]cos(60) = \frac{a}{\frac{15}{2}}[/tex]
[tex]a = cos(60)\frac{15}{2}[/tex]
[tex]a = \frac{15}{4}[/tex]
