for this problem we need the definition of law of sines
[tex] \frac{ \sin(a) }{a} = \frac{ \sin(b) }{b} = \frac{ \sin(c) }{c} [/tex]
therefore we can evaluate our knowns:
<G =74° with side unknown g
<H=58° with side 54
so we can set up the proportion
[tex] \frac{ \sin(74) }{g} = \frac{ \sin(58) }{54} [/tex]
then cross multiply and get the value of g
[tex]g \times \sin(58) = 54 \times \sin(74) [/tex]
therefore we get the value of g as
[tex]61.2 \: yards[/tex]
