Смежные стороны параллелограмма равны острый угол равен \( 30^{\circ} \). Найдите площадь параллелограмма. Сторона ромба равна 6 см, а один из углов равен \( 150^{\circ} \). Найди те площадь ромба.

Determine the standard equation of the ellipse using the stated information. Vertices of the major axis at \( (-1,9) \) and \( (-1,-11) \); length of the minor axis is 10 units. The standard equation of the ellipse is (Simplify your answer. Use integers or fractions for any numbers in the equation.)

\( \left. \begin{array} { l } { \frac { ( 1 - h ) ^ { 2 } } { a ^ { 2 } } + \frac { ( y - k ) ^ { 2 } } { b ^ { 2 } } = 1 } \\ { \frac { h ^ { 2 } } { a ^ { 2 } } + \frac { [ ( 3 - \frac { \pi } { 2 } ) - k ] ^ { 2 } } { b ^ { 2 } } = 1 } \\ { \frac { ( - 1 - h ) ^ { 2 } } { a ^ { 2 } } + \frac { ( 1 - k ) ^ { 2 } } { b ^ { 2 } } = 1 } \\ { \frac { ( - 5 - h ) ^ { 2 } } { a ^ { 2 } } + \frac { ( 3 - k ) ^ { 2 } } { b ^ { 2 } } = 1 } \end{array} \right. \)

In \( \triangle \mathrm{EFG}, e=96 \mathrm{~cm}, f=71 \mathrm{~cm} \) and \( \angle \mathrm{G}=52^{\circ} \). Find the length of \( g \), to the nearest centimeter.

In \( \triangle \mathrm{STU}, u=3.6 \) inches, \( s=7.9 \) inches and \( \angle \mathrm{T}=68^{\circ} \). Find the length of \( t \), to the nearest 10th of an inch.

In \( \triangle \mathrm{EFG}, e=880 \) inches, \( f=140 \) inches and \( g=890 \) inches. Find the measure of \( \angle \mathrm{G} \) to the nearest 10th of a degree.