In a triangle ABC: AB: BC = √2 / 2: angle A = 135. What is the angle C
| December 29, 2020 | education
Since AB / BC = √2 / 2, then let the side length AB = X * √2 cm, and the length of the BC side = 2 * X cm.
Let’s apply the sine theorem for a triangle.
AB / SinACB = BC / SinBAC.
X * √2 / SinACB = 2 * X / Sin135.
SinACB = X * √2 * (√2 / 2) / 2 * X = 1/2.
In triangle ABC, the angle BAC is obtuse, then the angle ACB <90.
Then the angle ACB = arcsin (1/2) = 30.
Answer: The angle ACB is 30.
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