In the triangle ABC AC = BC, AB = 4, cos A = 0.1. Find the speaker

Let’s draw the median CH from angle C to the base AB of an isosceles triangle. It will split the speaker in half:
AH = HB = (AB / 2) = 2, and will be the height.
Cosine is the ratio of the adjacent leg to the hypotenuse, i.e. in the ASN triangle:
cosА = АН / АС,
AC = AH / cosA = 2 / 0.1 = 20.

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