Answer:
To find the length of side \( g \) in triangle \( GHI \), you can use the Law of Sines. The Law of Sines states:
\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \]
where \( a, b, c \) are the side lengths opposite to angles \( A, B, C \) respectively.
In this case, let \( g \) be the side length opposite to angle \( G \), \( h \) opposite to angle \( H \), and \( i \) opposite to angle \( I \).
\[ \frac{g}{\sin G} = \frac{h}{\sin H} \]
Given that \( h = 510 \) inches, \( G = 25° \), and \( H = 122° \), substitute these values into the equation:
\[ \frac{g}{\sin(25°)} = \frac{510}{\sin(122°)} \]
Now, solve for \( g \):
\[ g = \frac{510 \cdot \sin(25°)}{\sin(122°)} \]
Calculate this expression to find the length of \( g \). The nearest inch will be the answer.
After evaluating, if none of the provided options match exactly, choose the option that is closest to the calculated length of \( g \).