Answer
a) θ=tan$^{-1}\frac{x}{4}$
b) θ=cos$^{-1}\frac{3}{x}$
Work Step by Step
a) Since the sides that are marked belong to the legs of the triangle, the trigonometric function that works here is tangent. Tangent is opposite over adjacent. So,
tan $θ=(\frac{x}{4})$
solving for θ gives:
$θ=$tan$^{-1}(\frac{x}{4})$
b) Since the sides that are marked are the adjacent and hypotenuse of θ, the trigonometric function that works here is cosine. Cosine is adjacent over hypotenuse. So,
cos $θ=(\frac{3}{x})$
solving for θ gives:
$θ=$cos$^{-1}(\frac{3}{x})$
