Questions: Find the acute angle (theta), to the nearest tenth of a degree, for the given functions values. [ sin theta=0.7692 ] (theta approx) - (Type an integer or a decimal rounded to the nearest tenth as needed.)

Solution Steps

To find the acute angle \(\theta\) given \(\sin \theta = 0.7692\), we need to use the inverse sine function (also known as arcsine). The result will be in radians, so we need to convert it to degrees and then round it to the nearest tenth.

We are given \(\sin \theta = 0.7692\).

To find \(\theta\), we use the inverse sine function: \[ \theta = \arcsin(0.7692) \approx 0.8776 \text{ radians} \]

Convert the angle from radians to degrees: \[ \theta \approx 0.8776 \times \frac{180}{\pi} \approx 50.2821^\circ \]

Round the angle to the nearest tenth of a degree: \[ \theta \approx 50.3^\circ \]

Final Answer