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MCIII Geo 2.17

 
 
Picture of Tina Jin
MCIII Geo 2.17
by Tina Jin - Tuesday, January 30, 2024, 6:52 AM
 

Hello,

For this one I solved an equation by law of cosines and got that h^2=36, 1, so h=6, 1. Clearly h=1 doesn't work because the angle is clearly obtuse. But somehow it still fits into the equation? Why? I know cos(45)=cos(-45), but clearly the angle isn't greater than 180.

Thanks,

Tina Jin

 
Picture of Dr. Kevin Wang
Re: MCIII Geo 2.17
by Dr. Kevin Wang - Tuesday, January 30, 2024, 9:12 AM
 

You need to show your whole equation.  The actual value of $h$ for $h^2=1$ in this question is $h=-1$.  No matter what method is used, it should end up with a quadratic equation $h^2 - 5h - 6=0$. My guess is that at some places you did a squaring of something, which brought in the extraneous solutions like $h=1$ and $h=-6$.

 
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