Use a calculator to find the acute angle alpha that satisfies the following equation. tanalpha =(5)/(7) alpha =square ^circ (Round to one decimal place as needed.)

To find the acute angle $\alpha$ that satisfies the equation $\tan\alpha = \frac{5}{7}$, we can use the inverse tangent function, also known as arctan or $\tan^{-1}$.<br /><br />The inverse tangent function allows us to find the angle whose tangent is a given value. In this case, we want to find the angle whose tangent is $\frac{5}{7}$.<br /><br />Using a calculator, we can find the value of $\alpha$ by taking the inverse tangent of $\frac{5}{7}$:<br /><br />$\alpha = \tan^{-1}\left(\frac{5}{7}\right)$<br /><br />Calculating this expression using a calculator, we get:<br /><br />$\alpha \approx 35.3^{\circ}$<br /><br />Therefore, the acute angle $\alpha$ that satisfies the equation $\tan\alpha = \frac{5}{7}$ is approximately $35.3^{\circ}$.