Math CentralQuandaries & Queries


Question from Yoonji:

the 3 sides of a triangular garden measure 200 ft., 250 ft., and 300 ft., respectively. the garden is to be divided by a line bisecting the longest side and drawn from the opposite vertex. what is the length of the bisecting line?


I drew a rough sketch of the garden with the bisecting line.


$|AB| = 250$ feet, $BC| = 200$ feet, $|CA| = 300$ feet and $D$ is the midpoint of $CA.$

In problems involving triangles you quite often have to use the Law of Sines or the Law of Cosines. Looking at the triangle $ABD,$ you know the lengths of $AB$ and $DA$ and hence if you knew the measure of the angle $DAB$ you could use the Law of Cosines to find the length of $BD.$ Can you use what you know about the triangle $ABC$ to determine the measure of the angle $DAB?$


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