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ONLINE CALCULATOR .A force of 187 pounds makes an angle of 73 degrees 36 ' with a second force. The resultant of the two forces makes an angle of 29 degrees 1 ' to the first force. Find the magnitudes of the second force and of the resultant.

User Terry Ryan
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1 Answer

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Answer:

The magnitudes of the second force is
Z = 129.9 N

The magnitudes of the resultant force is
R = 256.047 N

Step-by-step explanation:

From the question we are told that

The force is
F = 187 \ lb

The angle made with second force
\theta_o = 73 ^o 36' = 73 + (36)/(60) = 73.6^o

The angle between the resultant force and the first force
\theta _1 = 29 ^o 1 ' = 29 + (1)/(60) = 29.0167^o

For us to solve problem we are going to assume that

The magnitude of the second force is Z N

The magnitude of the resultant force is R N

According to Sine rule


(F)/(sin (\theta _o - \theta_1 ) = (Z)/(\theta _1)

Substituting values


(187)/(sin(73.3 - 29.01667)) =(Z)/(sin (29.01667))


267.82 =(Z)/(0.4851)


Z = 129.9 N

According to cosine rule


R = √(F ^2 + Z^2 + 2(F) (Z) cos (\theta _o) )

Substituting values


R = √(187^2 + 129.9 ^2 + 2 (187 ) (129.9) cos (73.6))


R = 256.047 N

User Brandon Deo
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