Given: A right triangle with sides
[tex]\begin{gathered} a=81\text{ mm} \\ c=99\text{ mm} \end{gathered}[/tex]
Required: To determine the measure of the angle
[tex]\beta[/tex]
Explanation: The measure of the required angle can be determined by using the trigonometric ratio cosine as follows-
[tex]cos\beta=\frac{a}{c}[/tex]
Substituting the values of a and b as-
[tex]\begin{gathered} cos\beta=\frac{81}{99} \\ =\frac{9}{11} \end{gathered}[/tex]
Hence, the angle is-
[tex]\beta=cos^{-1}(\frac{9}{11})[/tex]
Thus-
[tex]\begin{gathered} \beta=35.0968\degree \\ \beta\approx35.10\degree \end{gathered}[/tex]
Final Answer: The measure of the angle is-
[tex][/tex]
