Question

Which is correct for finding the cm of angle z? Show steps please!! Urgent!

Answer 1

Answer:

$\large\boxed{b.\ \angle z=\cos^{-1}\dfrac{55}{73}}$

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.

$48^2+55^2=73^2\\\\2304+3025=5329\\\\5329=5329$

For angle z:

$opposite=48\\adjacent=55\\hypotenuse=73$

$sine=\dfrac{opposite}{hypotenuse}\\\\cosine=\dfrac{adjacent}{hypotenuse}\\\\tangent=\dfrac{opposite}{adjacent}$

Substitute:

$\sin(\angle z)=\dfrac{48}{73}\to\angle z=\sin^{-1}\dfrac{48}{73}\\\\\cos(\angle z)=\dfrac{55}{73}\to \angle z=\cos^{-1}\dfrac{55}{73}\\\\\tan(\angle z)=\dfrac{48}{55}\to\angle z=\tan^{-1}\dfrac{48}{55}$