Final answer:
The accurately represent the height of the Gateway Arch, the model will need to be 155 inches tall.
Step-by-step explanation:
To determine the height of the model, we need to use the scale ratio.
The scale ratio given is 1/2 yd = 1/4 in.
This means that for every 1/2 yard in the actual Gateway Arch, the model will represent 1/4 inch.
Since the height of the Gateway Arch is 310 yards, we can set up a proportion to find the height of the model. Let x represent the height of the model:
1/2 yd / 1/4 in = 310 yd / x in
To simplify this proportion, we can multiply both sides by 1/2 and 1/x:
1/4 in = (310/2) yd / x in
Now, we can cross-multiply and solve for x:
x = (1/4) * (x/ (310/2))
x = 155/yd
Therefore, the model will need to be 155 inches tall to accurately represent the height of the Gateway Arch.