Problema Solution
a box weighing 80 pounds is hanging from the end of a rope. The box is pulled sideways by a horizontal rope with a force of 24 pounds. What angle, to the nearest degree, does the first rope make with the vertical?
Answer provided by our tutors
We can consider the 80 pound vertical force of the box and the horizontal force of 24 pounds as a sides of a right triangle with legs
a = 80 and b = 24.
We need to find the angle between 'a' and the hypotenuse. Lets denote that angle with 'A' thus we have
tan A = b/a
tan A = 80/24
A = arctan 0.3
A = 0.29 rad
A = 17 degrees approximately
The angle between the first rope and the vertical is 17 degrees.