Answer:
Vector (ordered pair - rectangular form)
![\vec F = (27.189,12.679)\,[lbf]](https://tex.z-dn.net/?f=%5Cvec%20F%20%3D%20%2827.189%2C12.679%29%5C%2C%5Blbf%5D)
Vector (ordered pair - polar form)

Sum of vectorial components (linear combination)
![\vec F = 27.189\cdot \hat{i} + 12.679\cdot \hat{j}\,[N]](https://tex.z-dn.net/?f=%5Cvec%20F%20%3D%2027.189%5Ccdot%20%5Chat%7Bi%7D%20%2B%2012.679%5Ccdot%20%5Chat%7Bj%7D%5C%2C%5BN%5D)
Step-by-step explanation:
From statement we know that force exerted on the wagon has a magnitude of 30 pounds-force and an angle of 25° above the horizontal, which corresponds to the +x semiaxis, whereas the vertical is represented by the +y semiaxis. 
The force ( ), in pounds-force, can be modelled in two forms:
), in pounds-force, can be modelled in two forms:
Vector (ordered pair - rectangular form)
 (1)
 (1)
Vector (ordered pair - polar form)

Sum of vectorial components (linear combination)
 (2)
 (2)
Where:
 - Norm of the vector force, in newtons.
 - Norm of the vector force, in newtons.
 - Direction of the vector force with regard to the horizontal, in sexagesimal degrees.
 - Direction of the vector force with regard to the horizontal, in sexagesimal degrees.
 ,
,  - Orthogonal axes, no unit.
 - Orthogonal axes, no unit.
If we know that  and
 and  , then the force exerted on the wagon is:
, then the force exerted on the wagon is:
Vector (ordered pair - rectangular form)
![\vec F= \left(30\cdot \cos 25^{\circ}, 30\cdot \sin 25^{\circ}\right)\,[lbf]](https://tex.z-dn.net/?f=%5Cvec%20F%3D%20%5Cleft%2830%5Ccdot%20%5Ccos%2025%5E%7B%5Ccirc%7D%2C%2030%5Ccdot%20%5Csin%2025%5E%7B%5Ccirc%7D%5Cright%29%5C%2C%5Blbf%5D)
![\vec F = (27.189,12.679)\,[lbf]](https://tex.z-dn.net/?f=%5Cvec%20F%20%3D%20%2827.189%2C12.679%29%5C%2C%5Blbf%5D)
Vector (ordered pair - polar form)

Sum of vectorial components (linear combination)
![\vec F = (30\cdot \cos 25^{\circ})\cdot \hat{i} + (30\cdot \sin 25^{\circ})\cdot \hat{j}\,[N]](https://tex.z-dn.net/?f=%5Cvec%20F%20%3D%20%2830%5Ccdot%20%5Ccos%2025%5E%7B%5Ccirc%7D%29%5Ccdot%20%5Chat%7Bi%7D%20%2B%20%2830%5Ccdot%20%5Csin%2025%5E%7B%5Ccirc%7D%29%5Ccdot%20%5Chat%7Bj%7D%5C%2C%5BN%5D)
![\vec F = 27.189\cdot \hat{i} + 12.679\cdot \hat{j}\,[N]](https://tex.z-dn.net/?f=%5Cvec%20F%20%3D%2027.189%5Ccdot%20%5Chat%7Bi%7D%20%2B%2012.679%5Ccdot%20%5Chat%7Bj%7D%5C%2C%5BN%5D)