Question

a triangle has two sides that measure 10 in. and 8 in. which could be the measure of the third side?

Answer 1

if the triangle has a right angle, the measure of the third side is 12.8 inches

Answer 2

Solutions

To solve this problem we have to use the Pythagorean theorem. You can only use the Pythagorean theorem in Right Triangles. The longest side of the triangle is called the "hypotenuse". C² is the longest side so it is the hypotenuse . To calculate c² we have to do α² + β² = c². 

Given 

Side (A) = 10 in 
Side (B) = 8 in 
Side (C) = unknown 

The length of the third side must be greater than 0 but less than 18in 

10-8 < s < 10+8

2 < s < 18 

17 in is the correct answer