In triangle ABC, angle C is 90, BC = 2, cosA = √17 / 17. find AC.
| July 26, 2021 | education
From the known cos (A), we find sin (A):
sin (A) = √ (1 – cos ^ 2 (A)) = √ (1 – (√17 / 17) ^ 2) =
= √ ((17 ^ 2 – 17) / (√17 ^ 2)) = √ ((289 – 17) / 17 =
= √272 / 17 = √ (16 * 17) / 17 = 4√17 / 17;
sin (A) = BC / AC;
AC = BC / sin (A) = 2 / (4√17 / 17) = 34 / (4√17) = (2 * 17) / 4√17 = √17 / 2.
Answer: AC = √17 / 2.
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