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Moderate

Law of Sines or Cosines

ACTMAT-4O3KYX

The figure below represents a water molecule, where $H$ represents an hydrogen molecule and $O$ represents an oxygen molecule:

If the distance between each hydrogen molecule and the oxygen molecule (as measured from their centers) is 0.9584 angstroms, what is the distance (in angstroms) between the two hydrogen molecules (measured from their centers)?

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 $c$: $2=a$, $2+b$, $2-2ab\cos{C}$, and the Law of Sines states that:

$$\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}$$

A

$1.174$

B

$1.355$

C

$1.41$

D

$1.515$

E

$1.66$