Measuring the diameter of the moon

Classical Mechanics Level 2

Did you know you can approximate the diameter of the moon with a coin $($ of diameter $d)$ placed a distance $r$ in front of your eye?

If the distance between the moon and your eye is $R,$ what is the diameter of the moon?

\frac{R}{dr}

\frac{r}{R}d

\frac{R}{d}r

\frac{R}{r}d

4 solutions

Discussions for this problem are now closed

Shabarish Ch
Mar 21, 2014

On observation, we see that a triangle is formed between the eye and the coin's diameter and another triangle is formed between the eye and the moon's diameter. Using standard geometry, we can prove that these two triangles are similar. So, using the properties of similar triangles,

$\frac{r}{R} = \frac{d}{D}$

$D = \frac{R}{r} d$

there is the good answer and i'm not totally agree with you.

Angelena Coralie - 7 years, 2 months ago

(D/2)/RsinФ=(d/2)/rsinФ then D/R=d/r then D=dR/r

Ashok Aryan - 7 years, 2 months ago

Simple:

Using the tangent rule:

d =. D ---- ---- 2r. 2R

So, D = dR ------- r

Misbah Yahya - 7 years, 2 months ago

based on the properties of similar triangles i.e., in similar triangles the ratio of the corresponding sides are equal,
D/d=R/r,
D= Rd/r

Vln Gupta Sreekakolapu - 7 years ago

Trixie Vasquez
Mar 29, 2014

Ewol Sayson
Apr 1, 2014

Well its a problem about similar figures.

we an see that it makes similar triangles therefore

r /d = R/D

by solving fractions u'll get D= Rd/r

hee

DaNyal Al-lmed
Mar 31, 2014

here R (the distance b/w the moon and eye) is inversly proportional to 1/r (distance b/w eye and coin) so Rx1/r=R/r case solver :"p

Measuring the diameter of the moon

4 solutions

Discussions for this problem are now closed

0 pending reports