Question

What is the value of g?

Answer 1

Apply the Law of Sines here.    

    54 yd                     g
----------------- = ------------------
 sin (58 deg)       sin (74 deg)

Do the math.  Cross mult. first, and then solve for g:
                                          
                                           54 sin 74
54 sin 74 = g sin 58;   g = --------------- = ?
                                            sin 58

Answer 2

Answer: 61.2 yd

Step-by-step explanation:

In the given triangle GHJ, we have

∠G=74° , GJ= 54 yd  , ∠H=58° , HJ =g

To find the value of g we apply the law of sines we get,

$\frac{g}{\sin(74^{\circ})}=\frac{54}{\sin(58^{\circ})}\\\\\Rightarrow g=\frac{\sin(74^{\circ})\times54}{\sin(58^{\circ})}\\\\\Rightarrow\ g=\frac{(0.96126169593)54}{0.84804809615}\\\\\Rightarrow\ g=61.2089477187\approx61.2\ yd$

 Hence, the value of g = 61.2 yd.