Question 1078335
 from a hang glider approaching a 5000 ft. clearing
 the angles of depression of the opposite ends of the field measure 24° & 30°.
 How far is the hang glider from the nearer end of the field?
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Draw this out,  the interior angle opposite 5000 ft is 30-24 = 6 degrees
the alternate angle of parallel lines is 24 degrees opposite the side (a) of the glider to nearest point of the clearing
:
We can us the law of sines
{{{a/sin(24)}}} = {{{5000/sin(6)}}}
Cross multiply, find the sines
.1045a = 5000 * .4067
a = {{{2033.683/.1045}}}
a = 19,456 ft from the nearest end
 
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