Two forces P and Q acts on a hook as shown.             Given: P = 100 N; θ1 = 19°If Q = 79 kN, find θ2 such that the resultant of the forces is horizontal to the right.QUESTION 7ANSWERA.20.34°B.23.43°C.24.04°D.24.34°

The problem involves two forces, P and Q, acting at angles θ1 and θ2 respectively. The resultant of these forces is horizontal to the right. This means that the vertical components of the forces must cancel each other out, while the horizontal components add up to give the resultant force.

The vertical and horizontal components of a force F at an angle θ can be found using the equations:

F_vertical = F * sin(θ) F_horizontal = F * cos(θ)

Given that P = 100 N and θ1 = 19°, we can find the vertical and horizontal components of P:

P_vertical = P * sin(θ1) = 100 * sin(19°) P_horizontal = P * cos(θ1) = 100 * cos(19°)

We know that Q = 79 kN = 79000 N, but we don't know θ2. However, we know that the vertical component of Q must be equal and opposite to the vertical component of P (since the resultant force is horizontal), and the horizontal component of Q must be equal to the resultant force minus the horizontal component of P.

Therefore, we can write:

Q_vertical = -P_vertical = -100 * sin(19°) Q_horizontal = Resultant_force - P_horizontal = Resultant_force - 100 * cos(19°)

Since Q_vertical = Q * sin(θ2) and Q_horizontal = Q * cos(θ2), we can solve these equations for θ2:

sin(θ2) = -P_vertical / Q = -100 * sin(19°) / 79000 cos(θ2) = Q_horizontal / Q = (Resultant_force - 100 * cos(19°)) / 79000

Finally, we can find θ2 using the equation:

θ2 = atan2(Q_vertical, Q_horizontal)

This will give the angle in radians, which can be converted to degrees by multiplying by 180/π. The correct answer will be the one that matches this calculated value of θ2.