A?a??daki dik koordinat düzleminde verilen ikizkenar ABO...

A?a??daki dik koordinat düzleminde verilen ikizkenar ABO üçgeninin bir kö?esi orijinde, di?er kö?eleri birim çember üzerindedir. B A(1,0) B" A' A" (1,0) B O ABD Üçgeni, birim çember içerisinde önce A'B'O' üçge- ni ile sonra A"B"O" üçgeni ile çak??acak biçimde hare- ket etmektedir. m($\widehat{BOA}$) = 20° oldu?una göre, B' noktas?n?n apsisi ile O" noktas?n?n apsisinin çarp?m? a?a??dakilerden hangisidir? $\frac{\cos 185^{\circ}}{2}$ A) $\frac{\cos 190^{\circ}}{2}$ B) $\frac{\sin 190^{\circ}}{2}$ C) D) tan190° E) $\frac{\sqrt{3}}{4}$

Transcript

00:01 Okay, our figure looks like this.

00:03 We're just given the one angle down below 44 degrees.

00:08 And we're also given that we've got these isosceles triangles on the left and right.

00:14 And we've got to find that angle on top.

00:17 So my strategy for these, rather than worrying about, well, how am i going to get that angle on the top? i just try to find everything that i can and about this triangle.

00:34 And unfortunately, i don't know a lot about that bottom triangle.

00:39 So that 44 doesn't seem to help me too much.

00:43 So let's start with the isosceles triangles.

00:45 Like let's say we already used x.

00:50 So i know the base angles of isosceles triangles are the same.

00:55 So what if i called this y, then this would have to be y.

00:59 Oh, and then notice we've got a vertical angle.

01:02 This would have to be y as well.

01:06 Okay, so now we've got kind of a connection to that 44 -degree angle.

01:11 How about the other isosceles triangle? let's call this z, and this one z, so then this would be z because they're vertical angles.

01:29 Okay, so i now know that y plus z plus 44 is 180, 180.

01:39 That might be useful.

01:42 How can we get the x involved? well, let's see.

01:48 I've got this larger triangle formed by bac, and i know those vertex angles would be, let's see, this one would be 180 minus 2y, and this one would be 180 minus 2z.

02:09 So i could say that x plus 180 minus 2y plus 180 minus 2z equals 180, and let's simplify that...

Question

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