Find the exact value of the expression. \[ \cos \left(\frac{5 \pi}{4}-\frac{7 \pi}{6}\right)=\square \]

In \( \triangle \mathrm{PQR}, p=4.7 \) inches, \( m \angle \mathrm{P}=76^{\circ} \) and \( m \angle \mathrm{Q}=57^{\circ} \). Find the length of \( q \), to the nearest 10th of an inch.

In \( \triangle \mathrm{FGH}, f=7.4 \) inches, \( g=1 \) inches and \( h=7 \) inches. Find the measure of \( \angle \mathrm{G} \) to the nearest degree.

In \( \triangle \mathrm{NOP}, n=54 \) inches, \( o=97 \) inches and \( p=95 \) inches. Find the measure of \( \angle \mathrm{N} \) to the nearest degree.

In \( \triangle \mathrm{GHI}, g=9.6 \) inches, \( m \angle \mathrm{I}=80^{\circ} \) and \( m \angle \mathrm{G}=15^{\circ} \). Find the length of \( h \), to the nearest 10th of an inch.

In \( \triangle \mathrm{TUV}, u=750 \mathrm{~cm}, m \angle \mathrm{~T}=105^{\circ} \) and \( m \angle \mathrm{U}=42^{\circ} \). Find the length of \( t \), to the nearest centimeter.