How do you solve the triangle given #triangleDEF, d=72, e=48, mangleF=110#?

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Answer 1 · 2018-02-26T08:36:50

#f = 99.2575, hat D = 43^@, hat E = 27^@#

Applying law of Cosines,

#f = sqrt(d^2 + e^2 - 2 d e cos F )#

#=> sqrt(72^2 + 48^2 - (2 * 72 * 48 * cos 110)) = 99.2575#

Applying law of sines,

#d / sin D = e / sin E = f / sin F#

#sin D = (d * sin F) / f = (72 * sin 110) / 99.2575 = 0.6816#

#hatD = sin ^-1 0.6816 = 43^@#

#hat E = 180 - 110 - 43 = 27^@#