[Math] How to solve the equation $5\sin x=12\cos x$

trigonometry

(I'm only a Year 7 so please tell me exactly how you found the solution)

Find the value of x when 5 sin x=12 cos x.

Round your number to the nearest degree.

I started by dividing both sides by cos x and then by 5 to get sin x/cos x but then I got stuck. I know that equation equals tan x but is that any help?

Best Answer

given is $$5\sin(x)=12\cos(x)$$ dividing by $$\cos(x)\ne 0$$ we obtain $$5\frac{\sin(x)}{\cos(x)}=12$$ dividing by $5$ we get $$\tan(x)=\frac{12}{5}$$ can you proceed?