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

Answer:

The magnitudes of the second force is   $Z = 129.9 N$

The magnitudes of the  resultant force is   $R = 256.047 N$

Explanation:

From the question we are told that  

    The force is  $F = 187 \ lb$

     The angle made with second force $\theta_o = 73 ^o 36' = 73 + \frac{36}{60} = 73.6^o$

     The angle between the resultant force and the first force $\theta _1 = 29 ^o 1 ' = 29 + \frac{1}{60} = 29.0167^o$

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

                $\frac{F}{sin (\theta _o - \theta_1 } = \frac{Z}{\theta _1}$

Substituting values

             $\frac{187}{sin(73.3 - 29.01667)} =\frac{Z}{sin (29.01667)}$  

             $267.82 =\frac{Z}{0.4851}$  

              $Z = 129.9 N$

According to cosine rule

       $R = \sqrt{F ^2 + Z^2 + 2(F) (Z) cos (\theta _o) }$

Substituting values

     $R = \sqrt{187^2 + 129.9 ^2 + 2 (187 ) (129.9) cos (73.6)}$

     $R = 256.047 N$