In triangle ABC, angle C is 90 *, angle A is 30 *, AC = 34√3. Find AB.
| September 11, 2021 | education
Let the leg BC = X cm, then the hypotenuse AB = 2 * X, since the leg lies opposite the angle 30.
By the Pythagorean theorem, AB ^ 2 = AC ^ 2 + BC ^ 2.
(2 * X) 2 = (34 * √3) 2 + X2.
4 * X ^ 2 – X ^ 2 = 3468.
3 * X ^ 2 = 3468.
X ^ 2 = 1156.
X = BC = 34 cm.
AB = 2 * 34 = 68 cm.
Answer: Side AB = 68 cm2.
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