Answer:
50.4 degrees
Step-by-step explanation:
Using sine rule
[tex]\frac {HI}{sin<G}=\frac {GI}{sin<H}=\frac {GH}{sin<I}[/tex]
Therefore, to find angle I
[tex]\frac {GI}{sin<H}=\frac {GH}{sin<I}[/tex]
Making angle I the subject of formula
[tex]I=sin^{-1}(\frac {GH sin<H}{GI})[/tex]
Substituting GH = 6, GI = 7, and m∠H = 64
[tex]I=sin^{-1}(\frac {6 sin64}{7})=50.389363496250\approx 50.39^{\circ}[/tex]
Therefore, angle I to the nearest tenth will be 50.4 degrees
