Respuesta :

Answer:

[tex]\Huge\boxed{x=53}[/tex]

Step-by-step explanation:

Hello There!

Once again we need 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 are given the adjacent side of x (45) and the hypotenuse (75) so we need to use cos

Remember cos = adjacent divided by hypotenuse

Now we create an equation

[tex]cos(x)=\frac{45}{75}\\\frac{45}{75} =.6[/tex]

now we have

[tex]cos(x)=.6[/tex]

like always we want to get rid of cos

to do so we take the inverse of cos (arccos^-1) and apply that to each side

[tex]arccos^-^1(cos(x))=x\\arccos^-^1(.6)=53.13010235[/tex]

finally we round to the nearest degree

we're left with x = 53

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