Точка F лежит на стороне AB треугольника ABC. Известно, что BC= 6, AC= 4, BF= 4, AF= 1. Найдите CF и cosA
To find CF, we can use the Pythagorean theorem. Let's label the length of CF as x. Applying the theorem, we get 6^2 + x^2 = (4 + 4)^2, which simplifies to 36 + x^2 = 64. Solving for x, we get x = 4. Therefore, CF = 4.To find cosA, we can use the Law of Cosines. Let's label the angle A as theta. Then, we have cos(theta) = (4^2 + 1^2 - 4^2) / (2*4*1), which simplifies to cos(theta) = 1/4. Therefore, cosA = 1/4.
Note that since the side lengths of the triangle are smaller than the sum of the other two sides, we can conclude that this is a valid triangle. This solution assumes that the point F lies between the segment AB and not on the extension of AB.
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