\( \sin (\alpha)=\frac{40}{41}, \alpha \) lies in quadrant I, and \( \sin (\beta)=\frac{12}{13}, \beta \) lies in quadrant II, a. \( \cos (\alpha+\beta)=\frac{1797}{41 \sqrt{1933}} \) (Simplify your answer. Type an exact answer, using radicalass needed. Use integers or fractions, for any b. \( \sin (\alpha+\beta)=\frac{-92}{533} \) (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any c. \( \tan (\alpha+\beta)=\square \)

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 \( \triangle \mathrm{PQR}, p=4.7 \) 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 \( \triangle \mathrm{TUV}, u=750 \mathrm{~cm}, m \angle \mathrm{~T}=105^{\circ} \) and \( m \angle \mathrm{U}=42^{\circ} \). Find the length of \( t \), to the nearest centimeter.

In \( \triangle \mathrm{EFG}, f=400 \) inches, \( m \angle \mathrm{~F}=94^{\circ} \) and \( m \angle \mathrm{G}=33^{\circ} \). Find the length of \( g \), to the nearest 10th of an inch.

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.