If a line sagged exerts 500 lbs of tension, what is the bisect tension when at a 60° corner?

• A. 500 lbs
• B. 866 lbs
• C. 1500 lbs
• D. 750 lbs

Answer: (B)

In this scenario, the concept of resolving tension forces into their components is key to understanding the correct answer. When a line experiences tension, it can be analyzed by breaking it down based on the angle at which it is positioned, particularly in relation to the vertical and horizontal components.

When tension is applied at a corner, it creates two lines of action which can be represented as vectors. In this case, the total tension of 500 lbs can be separated into two angles due to the presence of the 60° corner. By using trigonometric functions, we can determine the resultant tension at the bisecting angle.

To find the total tension where angle bisectors are involved, we utilize the sine and cosine rules. For an angle of 60°, the sine and cosine values relative to a 500 lbs tension lead to the calculation of the tension at bisecting lines. Specifically, we apply the formula for resultant tension:

Resultant tension = Tension / sin(θ)

Plugging in our values:

Resultant tension = 500 lbs / sin(30°), since bisecting a 60° angle results in a 30° angle.

Calculating this gives us:

Resultant tension = 500 lbs / 0.