Answer:
The explanation is given below.
Step-by-step explanation:
Given for a triangle to be obtuse only one of the angles must be shown to be obtuse but for a triangle to be acute all three angles must be shown to be acute.
According to Pythagoras theorem for a right angled triangle which has one angle of 90° rest of two are acute.
[tex]a^{2}+b^{2}=c^{2}[/tex]
Hence, by Pythagorean inequality
[tex]a^{2}+b^{2}>c^{2}[/tex]
which gives the triangle is acute.
Hence, one acute angle with the Pythagorean inequalities theorem shows that the triangle is acute.
