What is the largest angle in a triangle with sides 5, 12, 13? A) 75 degrees. B) 60 degrees. C) 90 degrees. D) 120 degrees.

According to the theorem, the largest angle in a triangle lies against the largest side, that is, opposite the side whose length is 13.

Let a = 13; b = 12; c = 5.

Let’s make an equation according to the cosine theorem: c ^ 2 = a ^ 2 + b ^ 2 – 2 * a * b * cos of the angle ab.

Substitute the values and find the cosine between side a and b: 169 = 144 + 25 – 120 * cos of the angle ab; 120 * cos angle ab = 0; cos = 0.

An angle whose cosine is 0 is 90 ° and 270 °, but since the sum of the angles in a triangle does not exceed 180 °, the maximum possible angle is 90 °.

Answer: S.