Step-by-step explanation:
YELLOW TRIANGLE:
[tex] \sin(30) = \frac{x}{12} \\ x = 12 \sin(30) = 6[/tex]
PURPLE TRIANGLE:
Since one of the angle is 45°, x = BC = 6
To prove:
[tex] \tan(45) = \frac{bc}{x} \\ bc = x \tan(45) = 6 \tan(45) = 6[/tex]
PINK TRIANGLE:
[tex] \tan(60) = \frac{bc}{y} \\ y = \frac{bc}{ \tan(60) } \\ = \frac{6}{ \tan(60) } \\ = 2 \sqrt{3} [/tex]
