Triangles

[FrozenDragon427]

Can someone help me with the second problem?

 

[Deleted member 4993]

Can someone help me with the second problem?

If I were to do the problem:

I would first sketch the triangle ABC and place point (P) inside and connect it to the vertices.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520​

Please share your work/thoughts about this problem.

 

[Dr.Peterson]

Can someone help me with the second problem?

One thing I did to solve it was to rotate the triangle with sides x, y, and s 60 degrees so two sides s coincide, and then think about what I saw. I'm sure there are lots of other ways.

 

[FrozenDragon427]

Ok, so what I did was try to solve it by attempting to make a right-angled triangle inside the equilateral triangle so that I can apply the Pythagoras theorem. Am I doing it right or do we solve it using another method?

 

[Dr.Peterson]

Ok, so what I did was try to solve it by attempting to make a right-angled triangle inside the equilateral triangle so that I can apply the Pythagoras theorem. Am I doing it right or do we solve it using another method? View attachment 21721

No, you can't assume the side of the equilateral triangle is z! No one said that segments x, y, and z form a right triangle themselves.

Did you try doing what I suggested? Rotate triangle APB by 60 degrees:

 

[FrozenDragon427]

No, you can't assume the side of the equilateral triangle is z! No one said that segments x, y, and z form a right triangle themselves.

Did you try doing what I suggested? Rotate triangle APB by 60 degrees:

View attachment 21730

I'm sorry but I can't understand what you're asking me to try

 

[Dr.Peterson]

Try looking for a right triangle in my version of the figure, and use that to solve for the red lines (which I called s). You'll probably need to draw at least one more auxiliary line.



Or else just try something else and show your work so we can guide you in the right direction. I'm sure mine isn't the only way to solve the problem.

But in any case, the goal is for you to do as much of the thinking as you can, in order to learn how to solve problems for yourself. This is not a small problem, so it will take some hard thinking to find the answer. Then you can take pleasure in your accomplishment!