Question

6. An office safe was lowered from an office building by two cables attached to buildings on opposite sides of a street. At one time the cables formed angles of 42° and 76°respectively, with the buildings. Find the pull on each of the cables if the safe weighed 1,250 pounds.

Answer 1

To find the pull on each of the cables, use the weight of the safe and the angles formed by the cables with the buildings.The pull on each of the cables that is approximately 836.41 unit and 122.86 unit.

Step-by-step explanation:

To find the pull on each of the cables, we can use the concept of forces and trigonometry. Let's call the angle formed by the first cable with the building A, and the angle formed by the second cable with the building B. We can then use the weight of the safe as the total force acting downward. The force exerted by each cable can be found using the sine function:

Force on first cable = Weight of safe * sin(A)
Force on second cable = Weight of safe * sin(B)

Given that angle A is 42°, angle B is 76°, and the weight of the safe is 1,250 pounds, we can substitute these values into the formulas to find the forces:

Force on first cable = 1,250 * sin(42°)

836.41 unit
Force on second cable = 1,250 * sin(76°)

=1212.86 unit

Calculating these values gives us the pull on each of the cables that is approximately 836.41 unit and 122.86 unit.