Q:

At what distance does a man, whose height is 2m subtend an angle of 10' ?

I tried using the angle in radian = length of arc/radius of circle and got the answer as 974.0286 m. But the answer given in the answer's section is 687.5m. What am I doing wrong? 

A:

Since no work was shown, it is hard to answer the question "What am I doing wrong?" However, providing a possible solution may give a clue.
$10'=\frac\pi{1080}$ is a small enough angle that
$$
\frac{\tan\left(\frac\pi{1080}\right)}{\frac\pi{1080}}=1.00000282
$$
So we need only compute
$$
\frac{2\text{m}}{\frac\pi{1080}}=687.55\text{m}
$$
and not have to worry about tangents, which is good since we might need $2\tan\left(\frac\pi{2160}\right)$ or $\tan\left(\frac\pi{1080}\right)$ depending on whether we are in line with the middle of the person or in line with the top of their head (and we are not given that information).

