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Hi there!

[tex]\large\boxed{AC \approx 483 ft}}[/tex]

AC is the hypotenuse, so we can use a trig formula to solve.

We are given the adjacent side, AB, so we must use cosine. Recall that:

cosθ = A/H

Thus:

cos(21.3) = 450 / H

Rearrange:

H = 450 / cos(21.3)

Use a calculator to evaluate:

H = 482.99 ≈ 483 ft.

Answer:

AC ≈ 483

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos21.3° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{450}{AC}[/tex] ( multiply both sides by AC )

AC × cos21.3° = 450 ( divide both sides by cos21.3° )

AC = [tex]\frac{450}{cos21.3}[/tex] ≈ 483 ( to the nearest whole number )