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

 
 
SUNCLAIRE的头像
Possible Kickstart to Question 1.29 of MC II-B Fall?
SUNCLAIRE - 2018年09月19日 Wednesday 17:10
 

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.

 
ReynosoDavid的头像
Re: Possible Kickstart to Question 1.29 of MC II-B Fall?
ReynosoDavid - 2018年09月20日 Thursday 11:37
 

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.

SUNCLAIRE的头像
Re: Possible Kickstart to Question 1.29 of MC II-B Fall?
SUNCLAIRE - 2018年09月20日 Thursday 15:37
 

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? 

LensmireJohn的头像
Re: Possible Kickstart to Question 1.29 of MC II-B Fall?
LensmireJohn - 2018年09月20日 Thursday 16:20
 

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 $8 - 5 = 3$.


SUNCLAIRE的头像
Re: Possible Kickstart to Question 1.29 of MC II-B Fall?
SUNCLAIRE - 2018年09月20日 Thursday 17:15
 

Thank you!