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Make a sketch, letting each side of the whole square be 2 (could be anything, so why not something simple ?)
let angle MAN = Ø , let angle BAM = angle DAN = y
in triangle ABM
AB = 2, BM = 1, then AM = √5 by Pythagoras
and sin y = 1/√5
at the right angle A
x + 2y = 90
x = 90 - 2y
take the sine of both sides
sinx = sin(90 - 2y)
but sin(90-2y) = cos 2y by the complementary angle theorem
and cos 2y = 1 - 2 sin^2 y
so
sinx = cos2y = 1 - 2(1/√5)^2
= 1 - 2/5
= 3/5 or .6
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don't know why I switched from Ø to x
so at top, let angle MAN = x
(I bet you could have figured that out yourself)
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Thanks a lot, sorry I am not too good at trigonometry
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Please do not post answers-only for other students' posts, especially those in which the other student has clearly not included any thinking on his/her own.
Posting only answers (especially with no explanation) doesn't teach anyone anything ... except maybe how to cheat!
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Stop cheating on your homework, it does not benefit you.
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stahp cheating
jk we encourage this
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YAY! GREAT!
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People, you realize that Richard Rusczyk is one of the founders of AoPs right.
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He's not one of the founder, he IS the founder.
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i like how its so easy to impersonate aops lol
