To find the length of side g in triangle FGH, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle.
Let's use the formula:
g / sin(G) = h / sin(H)
Substituting the given values:
g / sin(49°) = 840 / sin(93°)
Now, we can solve for g. Rearranging the equation, we have:
g = (sin(49°) * 840) / sin(93°)
Using a calculator, we can evaluate this expression to find the approximate length of g.
g ≈ (0.7502 * 840) / 0.9998
g ≈ 630.168 / 0.9998
g ≈ 630.227
Therefore, the length of side g, rounded to the nearest tenth of an inch, is approximately 630.2 inches.