Answer:
[tex]\large\boxed{b.\ \angle z=\cos^{-1}\dfrac{55}{73}}[/tex]
Step-by-step explanation:
Using the Pythagorean theorem, I justify that the angle y is a right angle. What I can not see in the picture.
[tex]48^2+55^2=73^2\\\\2304+3025=5329\\\\5329=5329[/tex]
For angle z:
[tex]opposite=48\\adjacent=55\\hypotenuse=73[/tex]
[tex]sine=\dfrac{opposite}{hypotenuse}\\\\cosine=\dfrac{adjacent}{hypotenuse}\\\\tangent=\dfrac{opposite}{adjacent}[/tex]
Substitute:
[tex]\sin(\angle z)=\dfrac{48}{73}\to\angle z=\sin^{-1}\dfrac{48}{73}\\\\\cos(\angle z)=\dfrac{55}{73}\to \angle z=\cos^{-1}\dfrac{55}{73}\\\\\tan(\angle z)=\dfrac{48}{55}\to\angle z=\tan^{-1}\dfrac{48}{55}[/tex]
