Respuesta :
The angle between the ropes is 58 degree , Option C is the right answer.
What is a Vector ?
Vector is an object that has both magnitude and direction.
It is given in the question that
[tex]\rm F_1 = 10000i +6000j\\F_2 = 13500 i -7000j\\[/tex]
The angle between the ropes can be calculated as
[tex]\overrightarrow F_1 * \overrightarrow F_2 = |F_1| *|F_2| cos \theta[/tex]
[tex]\rm F_1 = \sqrt{10000^2 + 6000^2}\\\\F_2 = \sqrt{ 13500^2 + 7000^2}[/tex]
[tex]\rm F_1\\[/tex] = 11662
[tex]\rm F_2[/tex] = 15207
[tex]\overrightarrow F_1 * \overrightarrow F_2 = (11662 * 15207)\; cos \theta[/tex]
[tex]\overrightarrow F_1 * \overrightarrow F_2[/tex] = 93000000
93000000 = 11662 * 15207 cos [tex]\rm \theta[/tex]
cos [tex]\rm \theta[/tex] =0.524
[tex]\rm \theta[/tex] = 58.37 degree
The angle between the ropes is 58 degree , Option C is the right answer.
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