Use the law of sines to show if a triangle with:[br][math]a=18[/math], [math]b=36[/math] and [math]\alpha=45°[/math] does exist or not.[br][br]Explain you reasoning below.
Applying the law of sines we have [math]\frac{18}{sin\left(45°\right)}=\frac{36}{sin\left(\beta\right)}[/math], and solving this equation we get [math]sin\left(\beta\right)=\frac{36\cdot sin\left(45°\right)}{18}=\sqrt{2}[/math]. [br]Since [math]\sqrt{2}[/math] is not in the interval [math]\left[-1,1\right][/math] of possible values for sine, this triangle can not exist.