Online Course Discussion Forum

Math II-A Geometry 1.29

 
 
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Math II-A Geometry 1.29
by Claire Zheng - Wednesday, 25 November 2020, 9:14 PM
 

Given that one of the angles of the triangle with sides (5, 7, 8) is 60°, show that one of the angles of the triangle with sides (3, 5, 7) is 120°. I don't really see how these two triangles are related. I think that the first triangle side with 7 is angle 60°, and 7 on the second triangle is also 120°. I have also tried connecting the two triangles together into a quadrilateral, the same integers sharing a side. I'm wondering if I could get a hint of how to solve this. Thank you.

 
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Re: Math II-A Geometry 1.29
by Dr. Kevin Wang - Wednesday, 25 November 2020, 11:56 PM
 

Very good observation that the angle opposite $7$ is $60^\circ$.  Also, great intuition to connect the two triangles sharing the side $7$!  Now, instead of putting the $(3,5,7)$ triangle outside the $(5,7,8)$ triangle, can you put it inside?