Answer:[tex]\displaystyle 37° ≈ m∠Z[/tex]Step-by-step explanation:First off, we have a right triangle, whose hypotenuse is 5 centimetres. So, by Pythagorean Triples, we know that the shorter leg [tex]\displaystyle [XA][/tex]is 3 centimetres and the longer leg [tex]\displaystyle [ZX][/tex]is 4 centimetres. If you are still uncertain about this, you can just simply check this with the Pythagorean Theorem:[tex]\displaystyle a^2 + b^2 = c^2 \\ \\ 3^2 + 4^2 = 5^2 → 9 + 16 = 25[/tex]☑Since this is a genuine statement, 5, 3, and 4 are authentic Pythagorean Triples.Now that we got that cleared up, we can now try to figure out how to solve for the m∠Z, which would be to use a trigonometric ratio. Now this is a tricky one because although we are given that the cosine function needs to be used, we have to use its inverse because we are solving for an angle measure. If we were solving for a side, then we would use the regular cosine function, but we do not in this case. Anyway, here is how it is done:[tex]\displaystyle sec^{-1} \: 1\frac{1}{4} ≈ 36,86989765 ≈ 37° \\ \\ OR \\ \\ cos^{-1} \: \frac{4}{5} ≈ 36,86989765 ≈ 37°[/tex]Now, you see what I did? SURPRISE! I intentionally did the secant ratio as well, to show you that you could have also solved this using the secant ratio because secant and cosine are multiplicative inverse trigonometric ratios.EXTENDED INFORMATION ON TRIGONOMETRIC RATIOS[tex]\displaystyle \frac{OPPOSITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOSITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOSITE} = csc\:θ \\ \frac{ADJACENT}{OPPOSITE} = cot\:θ[/tex]I am joyous to assist you anytime.