1. ## triangle

https://www.examinations.ie/schools/...gher_Level.pdf

I am stuck on question Q8aii ive been told that the angle is greatest vale a can have is when it makes a right angled (triangle ACF)
i wondering why this is .

2. ## Re: triangle

Calculate the limit of $\alpha$ as $|DE| \to 0$.

3. ## Re: triangle

One rather obvious point should be that the support attached to the back only works when the panel is tilted toward the back! If $\displaystyle \alpha> 90$ degrees the panel will fall over forwards.

4. ## Re: triangle

I did not read the problem carefully enough. I apologize. Consider this: Draw a line segment perpendicular to AF that intersects point C. This represents the height of the triangle. Let's call the height of the triangle $h$. We know that $\sin \alpha = \dfrac{h}{25}$. So, the bigger $h$ is, the greater $\alpha$ is. Remember that if $h>22$, then the leg $CF$ would no longer touch the ground, so the maximum height is 22cm. Now, let's define $\angle CFA = \beta$. We know that $\sin \beta = \dfrac{h}{22}$. So, $h = 22\sin \beta$. The maximum value for $h$ is reached when $\beta = 90^\circ$ since that is when $h=|CF|=22$.

5. ## Re: triangle

Originally Posted by SlipEternal
I did not read the problem carefully enough.
Oh ya? Go stand in the corner....22 minutes....

6. ## Re: triangle

Originally Posted by DenisB
Oh ya? Go stand in the corner....22 minutes....
Most corners are 5400 minutes = 90 degrees. A corner that is 22 minutes? That would be really narrow... Where's my protractor?

7. ## Re: triangle

I'm still kinda confused
I do not see why angle AFC can not be slightly greater than 90 degrees and it would still not fall over. Like say 91 degrees

8. ## Re: triangle

If that angle is big then $\alpha$ is small. The question is not about the biggest angle you can get in the triangle. It is about the biggest you can make $\alpha$