In triangle ABC, side AB is 7 cm; angle B is 45 degrees; side BC is 5 cm. Find side AC.

Since, by condition, we have the lengths of the two sides of the triangle and the angle between them, we use the cosine theorem for triangles to find the length of the unknown side.

AC ^ 2 = AB ^ 2 + BC ^ 2 – 2 * AB * BC * Cos450 = 7 ^ 2 + 5 ^ 2 – 2 * 7 * 5 * √2 / 2 = 74 – 35 * √2.

AC = √ (74 – 35 * √2) = √ (74 – 49.5) = √24.5 ≈ 4.95 cm.

Answer: The length of the speaker side ≈ 4.95 cm.



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