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Possible Kickstart to Question 1.29 of MC II-B Fall?

Possible Kickstart to Question 1.29 of MC II-B Fall?

I have absolutely no idea how this question could possibly tie into what we are learning currently, other than how we can create a 30-60-90 triangle in the first triangle mentioned in the question. Could anyone possibly provide any kickstarters? I  do not want the answer to this question (just something to start it off!) and I apologize if I am not permitted to ask for help on questions, but I am absolutely stumped on this question.

Re: Possible Kickstart to Question 1.29 of MC II-B Fall?

Hey Claire! No need to apologize, this is precisely why we have this forum. We are here to help!

Answering this question might help you: On the triangle with sides $(5,7,8)$, where is the $60^\circ$ angle? Recall the opposite side to the biggest (smallest) angle in a triangle is the biggest (smallest) side in the triangle. Now try drawing the other triangle inside this one.

Let us know if this helped or if you need another hint.

Re: Possible Kickstart to Question 1.29 of MC II-B Fall?

Unfortunately, no ideas were sparked in my mind although I did find the 60 degree angle in the first one and the 120 degree one in the second one. Could I possibly have a second hint?

Re: Possible Kickstart to Question 1.29 of MC II-B Fall?

I'll share some quick thoughts as well. Think about these in reference to the problem and the diagram you have so far.

1) An equilateral triangle has angles of $60^\circ$, hence the external angles are all $120^\circ$.

2) The first triangle has sides $(5, 7, 8)$ and we're looking at a triangle with sides $(3, 7, 8)$. It might be helpful to note that $8 - 5 = 3$.

Re: Possible Kickstart to Question 1.29 of MC II-B Fall?

Thank you!