14 I point A certain bridge arch is in the shape of half an ellipse 138 feet wide and 25 feet high. At what horizontal distance from the center of the arch is the height equal to 14.8 feet? Round your answer to one decimal place.

Step 1 ：The equation of an ellipse centered at the origin with a horizontal major axis is given by: \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\)

Step 2 ：In this case, a = 138/2 = 69 feet and b = 25/2 = 12.5 feet. So the equation of the ellipse is: \(\frac{x^2}{69^2} + \frac{y^2}{12.5^2} = 1\)

Step 3 ：We want to find the x-coordinate when the height y = 14.8 feet. Substituting y = 14.8 into the equation gives: \(\frac{x^2}{69^2} + \frac{14.8^2}{12.5^2} = 1\)

Step 4 ：Solving for x^2 gives: \(x^2 = 69^2 * (1 - \frac{14.8^2}{12.5^2})\)

Step 5 ：Taking the square root of both sides (and noting that x can be positive or negative because we're measuring distance from the center of the arch), we get: \(x = \pm69 * \sqrt{1 - \frac{14.8^2}{12.5^2}}\)

Step 6 ：Calculating this gives: \(x = \pm69 * \sqrt{1 - \frac{219.04}{156.25}}\)

Step 7 ：Simplifying further gives: \(x = \pm69 * \sqrt{1 - 1.401}\)

Step 8 ：Solving for x gives: \(x = \pm69 * \sqrt{-0.401}\)

Step 9 ：Since we can't have a negative square root in real numbers, it means that the height of 14.8 feet is not achievable in this ellipse. There seems to be a mistake in the problem as the maximum height of the ellipse is 12.5 feet, so it can't reach 14.8 feet. \(\boxed{\text{Error in the problem}}\)