In an isosceles triangle, the base is 15 cm long. The cosine of the angle between the sides is 7/16. What is the side side?

Since the triangle is isosceles, then AB = CB.

Let’s apply the cosine theorem for a triangle.

AC ^ 2 = AB ^ 2 + CB ^ 2 – 2 * AB * CB * CosABC.

152 = 2 * AB ^ 2 – 2 * AB ^ 2 * (7/16).

225 = 2 * AB ^ 2 * (1 – 7/16)

225 = 2 * AB ^ 2 * 9/16 = 9 * AB ^ 2/8.

AB ^ 2 = 225 * 8/9 = 200.

AB = CB = 10 * √2 cm.

Answer: The length of the side is 10 * √2 cm.




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