In triangle ABC, angle C is 90 degrees, AB = 5, tgA = 7/24. Find the AC.
| March 31, 2021 | education
tgBAC = 7/24 = BC / AC.
7 * AC = 24 * BC.
BC = 7 * AC / 24.
By the Pythagorean theorem, AC ^ 2 = AB ^ 2 – BC ^ 2.
AC ^ 2 = AB ^ 2 – (7 * AC / 24) ^ 2.
AC ^ 2 + 49 * AC ^ 2/576 = AB ^ 2.
625 * BC ^ 2/576 = 25.
BC ^ 2 = 25 * 576/625.
BC = 5 * 24/25 = 24/5 = 4.8 cm.
Answer: The length of the speaker side is 4.8 cm.
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