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)#.