10 units up and 7 units left transformation

The diagram is attached below.

The hypotenuse is 16 feet, and the vertical leg of the triangle created by the ladder is 13.8 feet. We are looking for the angle opposite of the 13.8 ft side.

To find this angle, we will need to use an inverse trigonometric function. The function we will use is sine, because we are given the opposite side and hypotenuse.

sin(x) = 13.8 / 16

x = sin^-1(13.8 / 16)

x = 59.5985 degrees (feel free to round to wherever you need)

Yes, the ladder will be safe at this height, because 59.6 degrees is less than 65 degrees.

Hope this helps!! :)