Math CentralQuandaries & Queries


Question from Darya., a student:

Hello! I need a solution...

How to find third side of irregular triangle if c = 17m, b = 28m and area S = 210m^2.


Use the formula

$S = \frac12 b c \sin A,$ where $S$ is the area, to find the angle A between edges b and c.

Then use the cosine law

$a^2 = b^2 + c^2 - 2 b c \cos A$ to find a.

Heron's formula (look it up!) leads to a solution too. While it involves solving a fourth degree equation for a, it is actually a quadratic in $a^2$ so can be solved fairly easily.

Good Hunting!

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