Let us determine what the sine of the angle A will equal, when from the condition of the assignment we know that the cosine of this angle is √10 / 10 (for this we use one of the trigonometric equations):
sin2 A = 1 – (√10 / 10) 2;
sin2 A = 90/100;
sin A1 = 3√10 / 10;
sin A2 = -3√10 / 10 (does not match the condition).
Let’s define what the tangent of angle A will be equal to:
tg A = 3√10 / 10: √10 / 10 = 3.
Let us determine what the side AH will be equal to:
6: 3 = 2.
So triangle ABC is isosceles, then CH is the median and then AB:
2 * 2 = 4.
Answer: 4 cm.
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