Its not so difficult.
tan-theta is equal to opposite side (side opposite the angle theta) divided by the adjecent side (angle next to the angle theta) of the triangle (the 2 that aren't the hypotamuse).
therefore tan theta is nothing more than 3/4.
If you were asked to find the angle theta it would be a simple equation, inverse tan of 3/4=inverse tan 0.75=36.87degrees, my original answer when I hadn't read the question. Its almost a trick question, students have spent years being asked to find theta but this question specifically tells them to stop early, before they reach my second paragraph. This is bound to throw people who work out theta when they're only asked for tan theta.
sin and cos have absolubtly nothing to do with this particular equation.
sin could be used to work out theta because inverse sin 3/5=inverse sin 0.6=36.87degrees=theta. cos could also be used to find theta because inverse cos 4/5=inverse cos 0.8=36.87degrees=theta.
But the question doesn't ask for theta, it asks for tan theta, therefore sin and cos are useless!
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Math is just a tool. Those guys at BBC are of the "tragic kind", if you ask me: as we could say here, chinese can be aces at math, but they are terrible dancers. We shall conquer all the nice girls, beat them racing at Shangai track AND solve their puny problems. Go, Juan Pablo! 
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