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Law of Cosines - Airplane Pilot

ACTMAT-XKIETO

The pilot of an airplane flying at an elevation of 12,000 feet sees a body of water ahead on radar at an angle of depression of $7°.$

At that same instant, the pilot of another airplane flying at an elevation of 10,000 feet sees the same body of water ahead on radar at an angle of $3°.$

See the figure below.

Approximately how far apart are the two planes, denoted by $x$ in the diagram?

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

$\text{2141 ft}$

B

$\text{2406 ft}$

C

$\text{92607 ft}$

D

$\text{93080 ft}$

E

$\text{93101 ft}$