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The moon is observed from two diametrically opposite points \( A \) and \( B \) on earth. The angle \( \theta \) subtended at the moon by the two directions of observation is \( 1^{\circ} 54^{\prime} \); given that the diameter of the earth to be about \( 1.276 \times 10^{7} \mathrm{~m} \). Compute the distance of the moon from the earth.
(a) \( 4.5 \times 10^{9} \mathrm{~m} \)
(b) \( 3.83 \times 10^{8} \mathrm{~m} \)
(c) \( 2.5 \times 10^{4} \mathrm{~m} \)
(d) \( 4 \times 10^{7} \mathrm{~m} \)
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