AMC 12A 2012 #10
Posted:
Fri Jun 15, 2012 9:37 pm
by nsguy1350
A triangle has area [unparseable or potentially dangerous latex formula], one side of length [unparseable or potentially dangerous latex formula], and the median to that side of length [unparseable or potentially dangerous latex formula]. Let [unparseable or potentially dangerous latex formula] be the acute angle formed by that side and the median. What is [unparseable or potentially dangerous latex formula]?
Re: AMC 12A 2012 #10
Posted:
Sat Jun 16, 2012 11:37 am
by darksaber21
I'm going to go ahead out on a limb here, and say that the height and the length of the median makes a triangle with the base, and to figure out the angle, we need the length of the height:
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
So, using the angle, I'm going to make a relationship between the height and the median, but as it turns out, they have a sine relationship, so I don't need to solve for [unparseable or potentially dangerous latex formula]:
[unparseable or potentially dangerous latex formula]