Question

Two forces with magnitudes of 150 and 100 pounds act on an object at angles of 40° and 170° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

Answer 1

This can not be solve without making a figure. It is a self explaining

Ref: Fig:



Note : 10 degrees = 180° - 170 (@100lb) = 10° (180 is straight line)

Sin 10° = D/100
D = 100 Sin 10
D = 17.36 lbs
Sin 40 = E/50
E = 40 Sin 40
E = 32.14 lbs

Cos 40 = G/50
G = 50 Cos 40
G = 38.3 lbs

Cos 10 ={G + I)/100
(G + I ) = 100 Cos 10
(G + I ) = 98.48 lb

I = (G + I) – G
I = 98.48 – 38.3
I = 60.18 lbs

Tan w = (E + D)/I
Tan w = ( 32.14 + 17.36) / 60.18
Tan w = 0.823
Direction:
=======================================...
W= 39.44 ° ◄ this is made from resultant Force & the Horizontal
=======================================...

Sin w = (E+D)/ Ft
Ft = (E+D)/Sin w
Ft = (32.14 + 17.36) Sin 39.44
Ft = (32.14 + 17.36) 0.64

=======================================...
Ft ≈ 31.68 lbs ◄ Ans (Resultant Force:)
=======================================...

Hope this helps
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God Bless

Answer 2

here is the figure(-:
http://prntscr.com/3rvlil

Answer 3

Thank you so much for the thorough explanation!
I wish you clear skies!