Questions: Find x. Round your answer to the nearest tenth of a degree.

Solution Steps

In the given right triangle, we need to find the angle \( x \). We have the lengths of the opposite side (7) and the hypotenuse (9). The appropriate trigonometric ratio to use is the sine function, which is defined as: \[ \sin(x) = \frac{\text{opposite}}{\text{hypotenuse}} \]

Using the sine function, we set up the equation: \[ \sin(x) = \frac{7}{9} \]

To find the angle \( x \), we take the inverse sine (arcsine) of both sides: \[ x = \sin^{-1}\left(\frac{7}{9}\right) \]

Using a calculator to find the inverse sine: \[ x \approx \sin^{-1}(0.7778) \approx 51.1^\circ \]

Final Answer