Exercise 21 Page 720

We are given that a curved road is part of $\circ C,$ which has a radius of $88$ feet. Let's take a look at the given diagram.

To find $AB$ let's recall that if the radius of a circle is perpendicular to a chord, then it bisects the chord and its arc. This means that $AE=EB.$

Now notice that $△AEC$ is a right triangle with a hypotenuse $AC,$ which is also a radius of $\circ C.$ Therefore $AC=88$ feet.

To find $EC$ we will use the fact that $DC=88$ — as this segment is also a radius — and $DE=15.$ Notice that by the Segment Addition Postulate the sum of $DE$ and $EC$ is equal to $DC.$ The length of $\overline{EC}$ is $73$ feet. Let's add this information to our diagram. Next we can find $AE$ using the Pythagorean Theorem. According to this theorem the sum of the squared legs of a right triangle is equal to its squared hypotenuse. Let's substitute the appropriate side lengths. Notice that since $AE$ is a side length, we will consider only positive case when taking the square root of $A{E}^2.$ The length of $\overline{AE}$ is approximately $49.14$ feet. Finally, as we noticed at the beginning, $AE=EB$ and the length $AB$ is two times $AE.$