# 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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