As can be seen from the condition of our problem, the AB side is the hypotenuse of the ABC triangle, at the same time the BC side is located opposite the angle whose cosine we know.
Let us determine what the sine of an angle will equal if from the condition of our problem we know exactly that its cosine is 5/6:
sin2 a = 1 – cos2 a;
sin2 A = 1 – (5/6) 2;
sin2 A = 1 – 25/36;
sin2 A = 11/36;
sin1 A = √11 / 6;
sin2 A = -√11 / 6 (not suitable).
Determine what is the length of the BC side:
25 * √11 / 6 = 25√11 / 6.
Answer: BC is equal to 25√11 / 6.
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