Kyle bought a ticket to see his favorite basketball team playing at home. His seat is in the terrace section, about 198 feet from the center of the court.If the angle of depression to the court is 57^circ , which of the following represents the hight Kyle is sitting? Round to the nearest tenth. About 107.84 ft. About 166.06 ft. About 236.09 ft. About 304.89 ft.

To solve this problem, we can use trigonometry. We are given the distance from Kyle's seat to the center of the court (198 feet) and the angle of depression to the court (57 degrees). We want to find the height of Kyle's seat.<br /><br />We can use the tangent function to find the height. The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of Kyle's seat and the adjacent side is the distance from his seat to the center of the court.<br /><br />The formula for the tangent function is:<br /><br />\[ \tan(\theta) = \frac{{\text{{opposite side}}}}{{\text{{adjacent side}}}} \]<br /><br />In this case, we have:<br /><br />\[ \tan(57^{\circ}) = \frac{{\text{{height}}}}{{198}} \]<br /><br />To solve for the height, we can rearrange the equation:<br /><br />\[ \text{{height}} = 198 \cdot \tan(57^{\circ}) \]<br /><br />Now we can plug in the values and calculate the height:<br /><br />\[ \text{{height}} = 198 \cdot \tan(57^{\circ}) \approx 198 \cdot 1.54 \approx 305.92 \]<br /><br />Rounding to the nearest tenth, the height of Kyle's seat is approximately 305.9 feet.<br /><br />Therefore, the correct answer is: About 304.89 ft.