Questions: If θ is an acute angle, solve the equation tan θ = 1/7. Express your answer in degrees, rounded to one decimal place.

Solution Steps

We start with the equation for the tangent of an angle \( \theta \): \[ \tan \theta = \frac{1}{7} \]

To find the angle \( \theta \), we use the arctangent function: \[ \theta = \tan^{-1}\left(\frac{1}{7}\right) \] Calculating this gives: \[ \theta \approx 0.1419 \text{ radians} \]

Next, we convert the angle from radians to degrees using the conversion factor \( \frac{180}{\pi} \): \[ \theta_{\text{degrees}} = \theta \times \frac{180}{\pi} \approx 0.1419 \times 57.2958 \approx 8.1301 \] Rounding this to one decimal place, we find: \[ \theta_{\text{degrees}} \approx 8.1 \]

Final Answer