Question

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.

Answer 1

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`