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,

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

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

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

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

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