মাত্রা ও একক বিষয়ক

The moon is observed from two diametrically opposite points on earth. The angle subtended at the moon by the two directions of observations is 1o541^o 54'. Given the diameter of the earth to be about 2.276×107m2.276 \times 10^7 m, compute the distance of moon from the earth.

হানি নাটস

Here D be the distance between the moon and the earth, d be the diameter of the earth.

Here, θ=1o54=1.9o=π180×1.9rad=0.033\theta=1^o54'=1.9^o=\dfrac{\pi}{180}\times 1.9 rad=0.033 radian

From the figure, tanθ=d/D\tan\theta=d/D

As θ\theta is very small, θ=d/D\theta=d/D

D=dθ=2.276×1070.033=6.84×108D=\dfrac{d}{\theta}=\dfrac{2.276\times 10^7}{0.033}=6.84\times 10^8 m

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