# Math Help - Keeping the ratio of the rectangle

1. ## Keeping the ratio of the rectangle

I need to find the size of the Green rectangle.

I am trying to cut the Green rectangle out between the parallel lines.

The Green rectangle has to be in the ratio of 27:10

I attempted using trigonometry, I calculated the angle between the diagonal line of the Green rectangle and its longer adjacent line is 22 degrees.

edit: The 220 cm line is perpendicular to the parallel lines. The 300 cm line is also the longer Green line extanded.

2. ## Re: Keeping the ratio of the rectangle

If you were to draw a line from the lower left corner, perpendicular to the two parallel lines, you would have a right triangle in which the 'near' side has length 220 cm and the hypotenuse has length 300 cm. Calling the angle, in the right triangle at that corner, $\theta$, we have $cos(\theta)= \frac{220}{300}= \frac{11}{15}$ so that $\theta= arccos\left(\frac{11}{15}\right)$. That means that the angle between the diagonal and the new perpendicular is $arccos\left(\frac{11}{15}\right)- 28$ degrees. So you now have a right triangle in which that diagonal is the hypotenuse, the angle is $arccos\left(\frac{11}{15}\right)- 28$ degrees, and the "near" leg has length 220 cm.

3. ## Re: Keeping the ratio of the rectangle

Thanks HallsofIvy,

I don't understand how you get 28 degrees, but I have solved the problem with similar approach.

I will remember to label the diagram next time!