(1) Joshua has a ladder that is 16 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 13.8 ft above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 65°.
What is the measure of this angle?
Will the ladder be safe at this height?
Show your work and draw a diagram to support your answer.

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!! :)