The square of the hypotenuse is not equal to the sum of the squares of the legs in a triangle with angles

The square of the hypotenuse is not equal to the sum of the squares of the legs in a triangle with angles: a) 45 and 60 degrees b) 45 and 45 degrees c) 47 and 43 degrees and why?

The square of the hypotenuse is equal to the sum of the squares of the legs only in right-angled triangles (that is, in which one angle is 90º).

Since the sum of the degree measures of all angles of any triangle is 180 degrees, we calculate from the presented triangles one that is not right-angled. To do this, we find the sum of the degree measures of these angles (in a right-angled triangle, their sum should be 90º):

A) 45º + 60º = 105º;

B) 45º + 45º = 90º;

B) 47º + 43º = 90º.

Since the first triangle is not right-angled, the square of its hypotenuse is not equal to the sum of the squares of the legs.

Answer: Option A.