A ladder leans up against a building that has a wall slanting away from the ladder at an angle of 96 degrees with the ground. If the bottom of the ladder is 23 feet from the base of the wall and it reaches a point 52 feet up the wall, how tall is the ladder to the nearest foot?

It is computing the 3rd side of a triangle with sides 23, 52 and angle between them 96 degrees. To compute the length of the ladder, use Carnot's formula c=\sqrt{a^2+b^2-2ab\cos \theta}
where a,b,c, are length of sides, and \theta the angle between sides a and b.