Answer:
[tex]\Huge\boxed{x=71.9}[/tex]
Step-by-step explanation:
Hello There!
Once again we are going to use trigonometry to solve for x
Here are the Trigonometric Ratios
sin = opposite divided by hypotenuse
cos = adjacent divided by hypotenuse
tan = opposite divided by adjacent
we need to find x and we are given its opposite side length (58) and the adjacent side length (19)
this corresponds with tangent so once again we will be using tangent to solve for x
Looking at tangent we see that its equal to opposite divided by adjacent so we create an equation
[tex]tan(x)=\frac{58}{19}\\\frac{58}{19} =3.052631579[/tex]
now we have
[tex]tan(x)=3.052631579[/tex]
Once again we need to get rid of the tan
to do so we take the inverse of tan ( tan^-1) and apply it to each side
[tex]arcsin^-^1(tan(x))=x\\arcsin^-^1(3.052631579)=71.86191784[/tex]
finally we round to the nearest tenth
we're left with x = 71.9
