The following image shows a problem out of my math book, Trigonometry, by Michael Corral (problem 13, section 1.3 for those who may be interested).
My analysis is that the $1.5$ (as far as I can tell) is an adjacent or opposite side, where as the hypotenuse is unknown. I can't see a use for $54^\circ$. However, judging from the dashed-split as shown, I'm thinking that's a hint suggesting the $54^\circ$ be divided in half. Still, even so I have yet to actually find and see where that potential $27^\circ$ should be used.
I've tried a number of things, from dividing the $2\frac18$ in half and using that to form a triangle with $1\frac12$, to using both whole fractions as their values and then setting the hypotenuse to be paralell with the radius, starting at the bottom tangent vertex. Still, no dice so far.
Can someone point me in the right direction in terms of how to solve this?