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Law of Cosines - 250 ft Water Tower

ACTMAT-VX1ESJ

A 250 foot tall water tower stands vertically on the side of a hill with an incline of $4°.$ To keep the tower from falling, two wires (denoted by $x$ and $y$ in the figure below) are tied to the top of the tower (one on each side) and secured at points 80 feet from the base of the tower.

How long is the wire labeled $x$?

Note: for any $ \triangle $ABC, where a is the opposite $ \angle $A, $b$ is the opposite $ \angle $B, and $c$ is the side opposite $ \angle $C}, the Law of Cosines states that $c$: $2=a$, $2+b$, $2-2ab\cos{C}$.

A

$\text{330 ft}$

B

$\text{268 ft}$

C

$\text{262 ft}$

D

$\text{257 ft}$

E

$\text{170 ft}$