In the triangle ABC the interior angle B equals 20 degrees and C 40 degrees. The length of the angle bisector through A is 2. What is the difference of the side lengths BC and AB?

Answer 1

AD is bisector of ∠BAC

m∠BAC = 120º

m∠BAD = m∠CAD = 60º

m∠BDA = 180º - 60º - 20º = 100º

2/BA = sin(20°)/sin(100°) ← Sine Law

BA = 2 • sin(100°)/sin(20°) ≅ 5.75877

BC/BA = sin(120º)/sin(40º) ← Sine Law

BC = BA • sin(120°)/sin(40°) ≅ 7.75877

Calculating the difference of the lengths of sides:

BC - BA = 7.75877 - 5.75877 ≅ 2