This is a rectangle, meaning that all angles are right angles and all sides opposite to one another have equal length.
Since the length of CD is 24, the length of AB must also be 24.
Angle B is a right angle because this is a rectangle.
See anything? I'll you a hint. We have a right triangle with only one missing value.
What do we use to solve for missing lengths in a right triangle? The Pythagorean theorem, of course!

The length of c (the hypotenuse) is 26.
The length of a (one leg) is 24.
The length of b is unknown and we want to find it.


Subtract 576 by both sides.

Take square root of both sides.

The length of the missing leg is 10, meaning that the length of BD is 10.
This is what you should be needing. Enjoy!
vi is going in the positive direction (up). (That's my choice). a (acceleration) is going in the minus direction (down). The directions could be reversed.
Givens
vi = 160 ft/s
vf = 0 (the rocket stops at the maximum height.)
a = - 9.81 m/s
t = ????
Remark
YOu have 4 parameters between the givens and what you want to solve. Only 1 equation will relate those 4. Always always list your givens with these problems so you can pick the right equation.
Equation
a = (vf - vi)/t
Solve
- 32 = (0 - 160)/t Multiply both sides by t
-32 * t = - 160 Divide by -32
t = - 160/-32
t = 5
You will also need to solve for the height to answer part B
t = 5
vi = 160 m/s
a = - 32
d = ???
d = vi*t + 1/2 a t^2
d = 160*5 + 1/2 * - 32 * 5^2
d = 800 - 400
d = 400 feet
Part B
You are at the maximum height. vi is 0 this time because you are starting to descend.
vi = 0
a = 32 m/s^2
d = 400 feet
t = ??
formula
d = vi*t + 1/2 a t^2
400 = 0 + 1/2 * 32 * t^2
400 = 16 * t^2
400/16 = t^2
t^2 = 25
t = 5 sec
The free fall takes the same amount of time to come down as it did to go up. Sort of an amazing result.