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Answer :
The angle between the resultant vector and the x-axis is approximately 43.5 degrees.
The x-component of the resultant vector R can be found by adding the x-components of the two vectors:
Rx = F cos(theta) + P cos(phi)
Substituting the values, we get:
Rx = 75 N cos(45 deg) + 66 N cos(54 deg)
Rx ≈ 114.8 N
The y-component of the resultant vector R can be found by adding the y-components of the two vectors:
Ry = F sin(theta) + P sin(phi)
Substituting the values, we get:
Ry = 75 N sin(45 deg) + 66 N sin(54 deg)
Ry ≈ 103.7 N
The magnitude of the resultant vector R can be found using the Pythagorean theorem:
|R| = √(Rx² + Ry²)
Substituting the values we calculated, we get:
|R| = √(114.8 N)² + (103.7 N)²
|R| ≈ 152.8 N
The angle between the resultant vector R and the x-axis can be found using the inverse tangent function:
θ = tan⁻¹(Ry / Rx)
Substituting the values we calculated, we get:
θ ≈ 43.5 deg
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