Determine the type of triangle (acute, rectangular, obtuse) if the sides are 10 cm, 14 cm and 17 cm.

We are given the lengths of the three sides of the triangle 10 cm, 14 cm and 17 cm and we need to find out what it is.

To solve the problem, we will apply the cosine theorem.

a ^ 2 = b ^ 2 + c ^ 2 – 2b * c * cos a.

We will not calculate the cos of the angle, we will only need to find its sign.

So, if cos a> 0, then a ^ 2 <b ^ 2 + c ^ 2 is an acute-angled triangle.

cos a = 0, a ^ 2 + b ^ 2 = c ^ 2 – rectangular triangle,

cos a <0, a ^ 2> b ^ 2 + c ^ 2 is an obtuse triangle, and a is the largest of the sides.

We calculate:

17 ^ 2> 10 ^ 2 + 14 ^ 2;

289> 100 + 169;

289> 269 – obtuse triangle.