In triangle ABC, angle C is 90, AC = 12, tgA = 2√10 / 3. Find AB.
| April 27, 2021 | education
Through the tangent of the angle BAC and leg AC, we determine the length of the leg BC.
ВС / АС = tgВАС.
ВС = АС * tgВАС = 12 * 2 * √10 / 3 = 8 * √10 / 3 cm.
By the Pythagorean theorem, we determine the length of the hypotenuse AB.
AB2 = AC2 + BC2 = 144 + 640 = 784.
AB = 28 cm.
Answer: The length of the hypotenuse AB is 28 cm.
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