In the following picture, $XY = YZ$, $\angle a = 40^\circ$, and the length opposite is $5$.
The problem asks to compute $XY$
We immediately dropped the dotted perpendicular and get two right triangles. The length of the bottom is 2.5 in each right triangle, and therefore $a/2 = 20^\circ$
$\sin 20 = 2.5 / XY$ or, $XY = 2.5 / \sin 20 \approx 7.3$
Their answer uses $5 / a = XY / 70$
$5 / 40 = XY / 70$ $XY = 350/40 = 8.75$
I would have thought both these answers should be the same, where did we go wrong?