<s>[INST] Find the two other sides in a 15-30-135 triangle A triangle has angle measures of 15, 30, and 135 degrees. The side opposite the 15 angle is x feet, the side opposite the 30 angle is y feet, and the side opposite the 135 angle is 2 feet.
Find x and y without the law of sine.
 [/INST] Apply sine rule in given triangle as follows 
$$\frac{x}{\sin 15^\circ}=\frac{y}{\sin 30^\circ}=\frac{2}{\sin 135^\circ}$$
considering first & third, 
$$\frac{x}{\sin 15^\circ}=\frac{2}{\sin 135^\circ}$$
$$x=\frac{2\sin 15^\circ}{\sin 135^\circ}=\frac{2\sin (45^\circ-30^\circ)}{\sin 45^\circ}=\frac{2\left(\frac{1}{\sqrt 2}\frac{\sqrt 3}{2}-\frac{1}{\sqrt 2}\frac{1}{2}\right)}{\frac1{\sqrt 2}}=\color{red}{\sqrt 3-1}$$
similarly, considering second & third, 
$$\frac{y}{\sin 30^\circ}=\frac{2}{\sin 135^\circ}$$
 $$y=\frac{2\sin 30^\circ}{\sin 135^\circ}=\frac{2\cdot \frac{1}{2}}{\frac{1}{\sqrt 2}}=\color{red}{\sqrt 2}$$
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