How do you find the exact value of the third side given $triangle DEF$ , $d=3.25, e=5.62, mangleF=58$ ?

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Answer 1 · 2017-01-13T12:35:10

$f~~4.7739 (4dp)$ .

We apply the the Cosine Rule to $Delta DEF$ to get,

$cos F=(d^2+e^2-f^2)/(2de)$ , or,

$f^2=d^2+e^2-2decos F$

$=3.25^2+5.62^2-2(3.25)(5.62)cos58$

$~~10.5625+31.5844-36.53(0.5299)$

$=42.1469-19.3572$

$=22.7897$

$:. f~~sqrt22.7897~~4.7739 (4dp)$ .

How do you find the exact value of the third side given triangle DEFtriangle DEF, d=3.25, e=5.62, mangleF=58d=3.25, e=5.62, mangleF=58?