Question

plse solve this

Answer 1

@dape Is this related to the biggest possible inscribed circle in the triangle?

Answer 2

A hint is that the points \((\cos\theta,\sin\theta)\) trace out the unit circle when \(0\leq\theta<2\pi\). So graph the lines, and draw in a unit circle, the answer should be clear then.

Answer 3

Here is a graph: http://www.wolframalpha.com/input/?i=plot+%7Bx%2By%3D2%2Cx-y%3D1%2C6x%2B2y%3D%E2%88%9A10%7D+from+x%3D-1+to+3%2C+y%3D-1+to+3+axes

Answer 4

Imagine a unit circle also drawn in the figure, you can see that all points \(0\le\theta\le\theta_{max}\) are included, where \(\theta_{max}\) is the angle where the unit circle crosses the brown/yellow line in the plot in the link that I posted. The thing left to do is to find that \(\theta_{max}\), which I'm sure you can manage.

Answer 5

srry , i cant find theta max

Answer 6

The thing is that at the intersection point it is both at the unit circle (\(x=\cos\theta_{max},\ y=\sin\theta_{max}\)) and on the line \(6x+2y=\sqrt{10}\). This is the equation system one has to solve to get the angle.

Answer 7

Okay, I did it this way, if we restrict our attention to the upper hemisphere of the unit circle, which is where our point is, we have that \(y=\sqrt{1-x^2}\). Combining this with the equation for the line (solve for y and put them equal) gives a second-degree equation, which is easy to solve. This will give you the x-coord of the point, now just take \(\arccos x=\theta_{max}\).