Question

Classify the triangle if the lengths of its sides are 8, 16, and 15. A Not a triangle B Acute C Right D Obtuse

Answer 1

Answer: Acute

Reason

A triangle is possible since adding any two sides leads to a sum larger than the third side (eg: 8+16 = 24 is larger than 15).

We have a triangle with sides a = 8, b = 15, c = 16. I made c the longest side.

Refer to the converse of the pythagorean theorem. There are 3 possible cases:

• If a^2 + b^2 = c^2, then we have a right triangle.
• If a^2 + b^2 < c^2, then the triangle is obtuse
• If a^2 + b^2 > c^2, then the triangle is acute

Notice how a^2+b^2 = 8^2+15^2 = 289 while c^2 = 16^2 = 256

Since 289 > 256, it leads to the a^2 + b^2 > c^2 case. Therefore, we have an acute triangle. All three angles are less than 90 degrees.