At its closest approach, Mars is about $5.6 * 10^7$ km from Earth and its apparent size is about 0.00012 radians. What is the approximate diameter of Mars?
What I did was divide 0.00012 radians by pi, and I got 0.00003819718 as the diameter, but I doubt this is the right answer. How do I apply the distance between Earth and Mars to find the diameter?
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$\begingroup$HINT: make a drawing of the Earth and Mars, and pick any point on Earth's surface. From that point, draw two lines, each ending in one of Mars's sides. The angle formed by those two lines is the said $0.00012$ radians. Since you know the height of that triangle, can you find its base?
$\endgroup$ $\begingroup$Since you are just looking for an approximation, we can just compute the arc length subtended by the angle.
The arc subtended by angle $\theta$ (in radians) at a radius $r$ has length $r\theta$.
Hence the diameter is $\approx 5.6 \times 10^7 \cdot 0.00012 \approx 6720$ km.
A more exact answer, which notes that the extreme rays touch Mars tangentially, shows that the diameter is $2 r \tan {\theta \over 2} \approx 6720$ km.
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