Find a value of \( \theta \) in the interval \( \left[0^{\circ}, 90^{\circ}\right] \) that satisfies the given statement. \( \cos \theta=0.75882011 \) \( \theta \approx \square^{\circ} \) (Simplify your answer. Type an integer or a decimal. Round to six decimal places if needed.

To find the value of \( \theta \) that satisfies \( \cos \theta = 0.75882011 \), you can use the inverse cosine function (arccos). Calculating this, we get: \[ \theta \approx \arccos(0.75882011) \approx 40.585757^{\circ} \] Rounding to six decimal places gives: \[ \theta \approx 40.585757^{\circ} \] So, the answer is: \(\theta \approx 40.585757^{\circ}\)