Final answer:
The correct choice for a ladder, based on the law of sines and additional stability considerations such as the angle and coefficient of static friction, would be answer 3: because the ladder is the correct length for the task, assuming all conditions for stability and safety are met.
Step-by-step explanation:
When choosing a ladder based on calculations using the law of sines or any other trigonometric calculations, one must also consider the stability and safety implications. If the result is independent of the length of the ladder, as stated in the reference material, the selection of ladder does not concern the length, but rather the stability, which depends on the ladder's weight, the angle with the floor, the net torque, and the coefficient of static friction. Hence, a correct ladder choice would be option 3: Yes, because the ladder is the correct length for the task, which assumes that the ladder's length satisfies the stability conditions and is suitable for the task it will be used for.
It is important to remember that safety is paramount, and the ladder must be stable and secure at the given angle and under the weight it needs to support. The coefficient of static friction plays a crucial role in preventing the ladder from slipping, which leads to the significance of this factor when calculating the forces involved and ensuring the ladder does not become unstable.