Answer:
f = 19.0
Step-by-step explanation:
By applying sine rule in the triangle given in the figure,
By applying triangle sum theorem,
m∠F + m∠G + m∠H = 180°
110° + m∠G + 40° = 180°
m∠G + 150° = 180°
m∠G = 30°
[tex]\frac{sin(\angle F)}{GH}= \frac{sin(\angle G)}{HF}=\frac{sin(\angle H)}{FG}[/tex]
[tex]\frac{sin(\angle 110^0)}{f}= \frac{sin(\angle 30^0)}{g}=\frac{sin(\angle 40^0)}{13}[/tex]
[tex]\frac{sin(\angle 110^0)}{f}= \frac{sin(\angle 40^0)}{13}[/tex]
[tex]\frac{0.9397}{f}= \frac{0.6428}{13}[/tex]
f = [tex]\frac{13\times 0.9397}{0.6428}[/tex]
f = 19.0
