Step-by-step explanation:
if it would be right-angled, the longest side is the Hypotenuse in the Pythagoras theorem
c² = a² + b²
c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.
if the square of the longest side (Hypotenuse) is greater than the sum of the squares of the two shorter sides, then the triangle is obtuse at the opposite angle of the Hypotenuse.
if the square of the longest side is less than the sum of the squares of the two shorter sides, then the triangle is acute.
if the square of the longest side is equal to the sum of the squares of the two shorter sides, then we have the Pythagoras theorem fulfilled, and the triangle is right angled (at the opposite angle of the Hypotenuse).
so,
83² = 71² + 48²
6889 = 5041 + 2304
6889 = 7345
and as we can see, that is wrong.
there is a difference of 456.
it is NOT right-angled.
the sum of the squares of the shorter sides is larger than the longest side.
therefore, the triangle is acute.
