In triangle ABC, angle c = 90 BC = 15 tgA = 3 √55 / 55 find AB.
| April 27, 2021 | education
Let’s use the definition of the tangent of an angle in a right-angled triangle and write it down, according to the condition.
Tg A = BC / AC.
We find the AU:
AC = BC / tg A = 15 / 3√55 / 55 = 15 * 55 / 3√55 = 5√55.
Both legs are known, by the Pythagorean theorem we find the hypotenuse:
AB = √ (AC² + BC²) = √ (25 * 55 + 225) = √ (1375 + 225) = √1600 = 40.
Answer: The hypotenuse AB is 40.
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