The student stared, blankly, at the sine rule problem in front of him.

$\frac{15}{\sin(A)} = \frac{20}{\sin(50^º)}$

“I don’t know where to st,” he started whining as something flew past his head. He knew better than to turn and look at whatever implement of death and destruction he had dodged. “I suppose I could cross-multiply…” he said.

The Mathematical Ninja put his head to one side. “Go on?”

“So $15 \sin(50º) = 20 \sin(A)$?”

Nod.

“And I can put that in the… smoking wreck of my calculator.”

“Oopsy,” said the Mathematical Ninja.

“Divide by fift… twenty,” he said. “So $\frac{15\sin(50^º)}{20} = \sin(A)$… and then could I inverse-sine it on the calculator?”

The Mathematical Ninja wrinkled his nose. “You could have done,” he admitted. “And you’d get about 35º.”

“Is there a quicker way to get to that sum?”

“I thought you’d never ask! Of course there is: it’s the sausage rule, and you can use it whenever you have an equation between two fractions.”

“Like this one!”

“The $\sin(A)$ is the only thing with a letter in.”
“Around the $15$ and the $\sin(50^º)$?”
”$\frac{15 \sin(50^º)}{20}$, which is equal to $\sin(A)$! Is that related to the Table of Joy, by any chance?”