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hiuwaitong@gmail.com
by Tonia Yuan - Sunday, October 29, 2023, 11:18 AM
 

For Math Challenge I-A geometry, I don't understand the following 

6.26; I don't know how to find the height for the 3 smaller equilateral triangles

6.30; I don't understand how they got the triangle with a hypotenuse length x is x2�2.

6.24; I don't know how the answer key got 37.5 degrees when the hexagon is outside the octagon when I got 15 degrees instead

6.22; I don't know how to do

p.s Maybe you can have the answer key to list the steps


 
Picture of Dr. Kevin Wang
Re: hiuwaitong@gmail.com
by Dr. Kevin Wang - Saturday, January 6, 2024, 1:45 AM
 

6.26: For equilateral triangles, as long as the side length is known, the height can be calculated the same way.  Remember the height splits the equilateral triangle into two $30$-$60$-$90$ triangles.

6.30: The corner is a $45$-$45$-$90$ triangle.  The side length ratio of such a triangle is $1:1:\sqrt{2}$.  If teh hypotenuse is $x$, it means $x$ corresponds to the $\sqrt{2}$ part, so the leg length is $\dfrac{x}{\sqrt{2}}$.

6.24: An interior angle of a regular octagon is $135^\circ$.

6.22: You can calculate all the angles of the quadrilateral.