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| Math Central | Quandaries & Queries |
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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. |
Darya,
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!
RD
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