# The sides of an isosceles triangle are 8 cm long and form an angle of 135 degrees. Find the length of the third side.

March 28, 2021 | education

| It is known:

Isosceles triangle;

Side = 8 cm;

The angle between the sides = 135 °.

Find the base of the isosceles triangle.

In order to find the third side, we apply the cosine theorem.

a ^ 2 = b ^ 2 + c ^ 2 – 2 * b * c * cos a;

Substitute the known values and find the third side of the triangle.

a ^ 2 = 8 ^ 2 + 8 ^ 2 – 2 * 8 * 8 * cos 135 ° = 64 + 64 – 2 * 64 * (-√2 / 2) = 64 + 64 – 1 * 64 * (-√2 ) / 1 = 64 + 64 + 64 * √2 = 128 + 64√2;

a ^ 2 = 128 + 64√2;

a = √ (128 + 64√2) = √ (128 + 64 * 1.4) = √ (128 + 89.6) = √217.6 = 14.8.

a = 14.8.

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