In the right triangle $\triangle{ABC}$ shown below, $AB=0$ units and $BC=12$ units. What is $\sin{A}$ ?

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Sine refers to the ratio of the opposite side to the hypotenuse. We can get the hypotenuse using the pythagorean theorem.

$$a^2+b^2 = c^2$$ $$9^2 + 12 ^2 = c^2$$ $$81+144 = c^2$$ $$225 = c^2$$ $$c= 15$$ $$\sin{A} = \frac{12}{15} =\boxed{\frac{4}{5}}$$

This triangle is similar to a 3-4-5 triangle. We can obtain the hypotenuse this way and then find the ratio of opposite to hypotenuse.

$$3(3)-3(4)-3(5) \implies 9-12-15$$