Hello!
For this type of problem, we are given a right triangle, and my go-to for finding a side length with another given side length and an angle value would most likely be the law of sines.
The law of sines states that:
[tex]\frac{a}{sin(A)}=\frac{b}{sin(B)}[/tex]
In the given triangle, the [tex]a[/tex] would be 45, and the opposite angle [tex]71[/tex], would be the [tex]A[/tex].
The same can be applied to the other side of the proportion.
[tex]x=b[/tex]
The opposite angle of side [tex]x[/tex] can be found using the definition of the combined angle of a triangle.
[tex]90+71+B=180[/tex]
[tex]B=19[/tex]
So now we can set up our proportion.
[tex]\frac{45}{sin(71)}=\frac{x}{sin(19)}[/tex]
[tex]x=sin(19)*\frac{45}{sin(71)}[/tex]
And we get that [tex]x[/tex] is around 15.5.
Hope this helps!
