vector question of physics

[Tweety-Angie]

Can somebody please answer me the formula or the method for the following question!

Q. Two forces 50N and 80N acts at a point P in anti-clockwise direction. The angle between the forces is 40 degree. Calculate the resultant force.
If the question is not clear, please have a look in the attachment, where I have drawn it. Then calculate the resultant of the two forces.
The question is extracted from physics book 'International A/As Level', Chapter-Physical quantities and Units, section 1.2, question no.7

 

[usman]

The system of forces given in the question is equivalent to the system in the attachment below.
All u need to do is to draw a parallelogram of forces as shown in the diagram.
Now, the angle PAB = 180 degrees - angle APQ(=40 degrees) [using alternate angles property]
= 140 degrees
The resultant of the two forces is equivalent to PB (same magnitude as well as direction), so u can determine the length of PB (although it is a force in newtons rather than a length bt for the purpose of the question, assume that it is a length measured in newtons.....;p). So, moving on, we observe that PAB is a triangle; with the angle PAB = 140 deg, PA = 80N, AB = 50N, PB = ?
Applying the cosine law,
(PB)^2 = (PA)^2 + (AB)^2 - 2(PA)(AB)cos(PAB)
= (80)^2 + (50)^2 - 2(80)(50)cos(140)
----> PB ~ 122.6N

 

[usman]

Attachment (vector question)

 

[princesszahra]

The system of forces given in the question is equivalent to the system in the attachment below.
All u need to do is to draw a parallelogram of forces as shown in the diagram.
Now, the angle PAB = 180 degrees - angle APQ(=40 degrees) [using alternate angles property]
= 140 degrees
The resultant of the two forces is equivalent to PB (same magnitude as well as direction), so u can determine the length of PB (although it is a force in newtons rather than a length bt for the purpose of the question, assume that it is a length measured in newtons.....;p). So, moving on, we observe that PAB is a triangle; with the angle PAB = 140 deg, PA = 80N, AB = 50N, PB = ?
Applying the cosine law,
(PB)^2 = (PA)^2 + (AB)^2 - 2(PA)(AB)cos(PAB)
= (80)^2 + (50)^2 - 2(80)(50)cos(140)
----> PB ~ 122.6N

right

 

[Tweety-Angie]

Thank-you Usman, it was so kind of you.
Well, how can we find the angle between the resultant force and one of the side?? Can anyone please help??

 

[DragonCub]

(Re) Solution to the angle size

This one is actually relatively simple. You just get to use trignometry.
Here, I've written it in a JPEG file as the attachment. Check it out and may my writing not confuse you

And by the way, I'm a new comer here. Glad to meet you buddy!

 

[Tweety-Angie]

Thank-you for your reply DragonCub.
And welcome here, glad to get you here.