Three forces with magnitudes pounds, pounds and pounds act on an object at angles respectively, with the positive x-axis.Find the direction and magnitude
Of the resultant force.(The choices below are given to two decimal places.)

Question

Three forces with magnitudes  pounds,  pounds and  pounds act on an object at angles  respectively, with the positive x-axis.Find the direction and magnitude
Of the resultant force.(The choices below are given to two decimal places.)

Quizplus · Accepted Answer

To find the magnitude of the resultant force, we can use the formula:
R^2 = F1^2 + F2^2 + F3^2 + 2F1F2cos(theta1-theta2) + 2F1F3cos(theta1-theta3) + 2F2F3cos(theta2-theta3)
where R is the magnitude of the resultant force, F1, F2, and F3 are the magnitudes of the three forces, and theta1, theta2, and theta3 are the angles they make with the positive x-axis. 
Substituting the given values, we get:
R^2 = (11ebbd4d_3efc_0fe7_8a0a_23c684f517e9_TB8202_11)^2 + (11ebbd4d_3efc_0fe8_8a0a_abae82fa979c_TB8202_11)^2 + (11ebbd4d_3efc_0fe9_8a0a_e32ca9b1f5de_TB8202_11)^2 + 2(11ebbd4d_3efc_0fe7_8a0a_23c684f517e9_TB8202_11)(11ebbd4d_3efc_0fe8_8a0a_abae82fa979c_TB8202_11)cos(11ebbd4d_3efc_0fea_8a0a_01d1a85fa8f1_TB8202_11 - 11ebbd4d_3efc_0feb_8a0a_af385181ca25_TB8202_11) + 2(11ebbd4d_3efc_0fe7_8a0a_23c684f517e9_TB8202_11)(11ebbd4d_3efc_0fe9_8a0a_e32ca9b1f5de_TB8202_11)cos(11ebbd4d_3efc_0fea_8a0a_01d1a85fa8f1_TB8202_11 - 11ebbd4d_3efc_0fec_8a0a_99ca17e143d7_TB8202_11) + 2(11ebbd4d_3efc_0fe8_8a0a_abae82fa979c_TB8202_11)(11ebbd4d_3efc_0fe9_8a0a_e32ca9b1f5de_TB8202_11)cos(11ebbd4d_3efc_0feb_8a0a_af385181ca25_TB8202_11 - 11ebbd4d_3efc_0fec_8a0a_99ca17e143d7_TB8202_11)
Simplifying this expression, we get:
R^2 = 781.06
Taking the square root, we get:
R = 27.96 lbs (approx)
The direction of the resultant force can be found using the formula:
tan(theta) = (F1sin(theta1) + F2sin(theta2) + F3sin(theta3))/(F1cos(theta1) + F2cos(theta2) + F3cos(theta3))
Substituting the given values, we get:
tan(theta) = (11ebbd4d_3efc_0fe7_8a0a_23c684f517e9_TB8202_11sin(11ebbd4d_3efc_0fea_8a0a_01d1a85fa8f1_TB8202_11) + 11ebbd4d_3efc_0fe8_8a0a_abae82fa979c_TB8202_11sin(11ebbd4d_3efc_0feb_8a0a_af385181ca25_TB8202_11) + 11ebbd4d_3efc_0fe9_8a0a_e32ca9b1f5de_TB8202_11sin(11ebbd4d_3efc_0fec_8a0a_99ca17e143d7_TB8202_11))/(11ebbd4d_3efc_0fe7_8a0a_23c684f517e9_TB8202_11cos(11ebbd4d_3efc_0fea_8a0a_01d1a85fa8f1_TB8202_11) + 11ebbd4d_3efc_0fe8_8a0a_abae82fa979c_TB8202_11cos(11ebbd4d_3efc_0feb_8a0a_af385181ca25_TB8202_11) + 11ebbd4d_3efc_0fe9_8a0a_e32ca9b1f5de_TB8202_11cos(11ebbd4d_3efc_0fec_8a0a_99ca17e143d7_TB8202_11))
Simplifying this expression, we get:
tan(theta) = -0.37
Taking the inverse tangent, we get:
theta = -19.12 degrees (approx)
Since the given angles are all in the first quadrant, the direction of the resultant force will be in the fourth quadrant (i.e. negative x-axis). Therefore, the answer is E, with the positive x-axis 11ebbd4d_3efc_36ff_8a0a_73e212fa01e1_TB8202_11.

Three Forces with Magnitudes Pounds, Pounds and