In triangle ABC, angle C = 90 *, BC = 5, tgA = 1/2 √2. Find AB
| June 2, 2021 | education
Let’s write down what is the tangent of an angle specifically for our case.
Tg ∠ A = BC / AC = 1/2 * √2.
Find the unknown leg AC.
AC = BC / 1/2 * √2 = 5 / 1/2 * √2 = 10 / √2 = 5√2.
Both legs are known; by the Pythagorean theorem, we find the hypotenuse AB.
AB² = BC² + AC² = 25 + 50 = 75.
AB = √75 = 5√3.
Answer: the hypotenuse AB is 5√3.
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