Answer
The truck can be at most $12 \ ft$ tall.
Work Step by Step
Let $y$ be the height of the truck.
The standard form of an ellipse can be written as: $\dfrac{x^2}{b^2}+\dfrac{y^2}{a^2}=1....(1); $ when $b \gt a$ has foci $(0, \pm c)$ where ; $c^2=a^2-b^2$
Now, we have $\dfrac{x^2}{100}+\dfrac{y^2}{225}=1$
We are given that $x=6 \ ft$
Therefore, $\dfrac{6^2}{100}+\dfrac{y^2}{225}=1 \implies \dfrac{36}{100}+\dfrac{y^2}{225}=1$
or, $y =12 \ ft$
Thus, the truck can be at most $12 \ ft$ tall.
