While holding the 80.0-n weight, the person raises his forearm until it is at an angle of 53.0 ∘ above the horizontal. if the biceps muscle continues to exert its force perpendicular to the forearm, what is this force when the forearm is in this position?

Hello

The weight of the object is W=80 N and points downwards, in the vertical direction. The force F exerted by the forearm is perpendicular to the forearm itself, which is at an angle of  above the horizontal; therefore, the angle between the direction of the force F and the direction of the weight P is also (but upwards). The component of the force F in the vertical direction is 

and  must be equal to the weight of the object to compensate it. Therefore we can write

and from this we can find the intensity of the force F: