A disabled automobile is pulled by means of two ropes as shown. Knowing that the tension in rope AB is 3 kN, determine by trigonometry the tension in rope AC and the value of α so that the resultant force exerted at A is a 4.8-kN force directed along the axis of the automobile.
Draw the force triangle.
Use cosines law to find the tension in rope AC.
Here, tension in the cable AB is and the resultant force is .
Substitute for and for.
Therefore, tension in the rope AC is.
Use law of sine to find the direction of the tension in rope AC.
Direction of the tension in rope AC is.