Question

A triangle has three sides: AB, BC, CA. We know that angle A is greater than angle C. Find the range for side AC.

A) AB< CA< BC
B) BC- AB < CA < AB + BC
C) BC< CA< AB
D) AB + BC < CA < BC- AB

Answer 1

BC- AB < CA < AB + BC

Explanation:

The sides opposite the larger angles are longer than the sides opposite smaller angles.

So, BC (opposite < A) is longer than AB (opposite < C) so,

BC > AB

The other side AC cannot be greater than AB + BC, otherwise the triangle would not exist, so,

AC < AB + BC

Also, CA > BC - AB

The range for AC is

BC- AB < CA < AB + BC