Determine the resultant force of two concurrent forces 100kn compressive,80 kn tensile acting at a point angle between the forces is 60 ͦ. also find angle made by resultant with 80 kn force.

To solve this problem, we will use the law of cosines and the law of sines.

Step 1: Convert the compressive force to a tensile force A compressive force is a force that attempts to compress an object. A tensile force, on the other hand, is a force that attempts to elongate an object. In this case, we can consider the compressive force as a negative tensile force. So, the 100 kN compressive force becomes -100 kN tensile.

Step 2: Use the law of cosines to find the resultant force The law of cosines is c² = a² + b² - 2abcos(C), where C is the angle between vectors a and b. In this case, a is 80 kN, b is -100 kN, and C is 60 degrees.

c² = (80)² + (-100)² - 280-100*cos(60) c² = 6400 + 10000 + 8000 c² = 24400 c = sqrt(24400) = 156.2 kN

So, the resultant force is 156.2 kN.

Step 3: Use the law of sines to find the angle made by the resultant with the 80 kN force The law of sines is a/sin(A) = b/sin(B) = c/sin(C). We want to find A, the angle opposite the 80 kN force.

sin(A) = asin(C)/c sin(A) = 80sin(60)/156.2 A = arcsin(80*sin(60)/156.2) = 30.6 degrees

So, the angle made by the resultant with the 80 kN force is 30.6 degrees.