In triangle \(ABC\), \(AB=5\), \(BC=8\), and the length of median \(AM\) is 4. Find \(AC\).

Thank you :D

proyaop Jan 31, 2022

#1**+4 **

I got \(\sqrt{39}\) with long equations and polynomials, can someone double check thanks!

proyaop Jan 31, 2022

#2**+2 **

Hi proyaop, yes your answer is correct.

Here is another method, using the cosine law twice only.

Consider triangle ABM, AB=5, AM=4 and BM = 4 (Because the median bisects the opposite side to the vertex).

So applying cosine rule gives you the angle ABC (which is the same as ABM)

Then, consider the triangle ABC, we have, AB=5 and BC=8 and we have the angle ABC.

Then apply cosine rule, yielding AC to be \(\sqrt{39}\)

Guest Jan 31, 2022