A12-foot ladder is placed 4 feet away from a house as shown. what is the value of x, rounded to the nearest degree? x ≈ ° according to the manufacturer, if the angle the ladder forms with the ground, x, is between 70° and 75°, then it meets safety standards. is this ladder being used safely?

Hello from MrBillDoesMath!

 x = 71 degrees. Yes, the ladder meets safety standards

Discussion:

The problem describes a right triangle with hypotenuse 12, the side against the ground is 4, and the angle between those two sides is "x".  For this triangle,

cosx = (side adjacent to angle) / hypotenuse

       =  4                                      / 12

       =   1/3

To find "x" take the inverse cosine of each side to find that :

x  is approximately 70.52 degrees. That's 71 degrees rounded to the nearest degree.

Thank you,

MrB