\( \theta \) is an angle in a right-angled triangle. \[ \theta=\tan ^{-1}(0.36) \] Work out the value of \( \theta \). Give your answer to 1 d.p.

To find the value of \( \theta \) where: \[ \theta = \tan^{-1}(0.36) \] we need to determine the angle whose tangent is 0.36. **Steps to Calculate \( \theta \):** 1. **Understanding the Tangent Function:** - The tangent of an angle in a right-angled triangle is the ratio of the opposite side to the adjacent side. - Therefore, \( \tan(\theta) = 0.36 \) implies that the opposite side is 0.36 times the length of the adjacent side. 2. **Using a Calculator:** - To find \( \theta \), we take the inverse tangent (also known as arctangent) of 0.36. - Ensure your calculator is set to **degrees** (since the answer is typically expected in degrees unless specified otherwise). 3. **Calculation:** \[ \theta = \tan^{-1}(0.36) \approx 19.8^\circ \] **Final Answer:** \[ \theta \approx 19.8^\circ \]