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

$\dfrac{3}{5}$

$\dfrac{3}{4}$

$\dfrac{4}{5}$

$\dfrac{5}{4}$

$\dfrac{4}{3}$

Approach 1

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

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

Approach 2

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.

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