Precalculus (6th Edition) Blitzer

Step 1. Based on the given conditions, assume the center of the road is the origin. We can write the equation of the ellipse as $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ with $a=\frac{30}{2}=15, b=10$ Step 2. The truck has a width of 10 feet; its upper right corner will have coordinates of $(5, 9.5)$ Step 3. At $x=5$, we have $\frac{5^2}{15^2}+\frac{y^2}{10^2}=1$, which gives $y^2=\frac{800}{9}$. Thus $y\approx9.4\ ft$ which means that the truck with a height of $9.5\ ft$ will not be clear to pass.