Answer: 4) 72
Step-by-step explanation:
First, we will draw a figure to represent the given situation. We can use a right triangle since we are given a floor, wall, and ladder. See attached.
Next, we will create an equation based on the given information. We are asked to find the angle the ladder makes with the ground, I have labeled this as theta (θ). Since this is a right triangle and we are given the opposite and the adjacent side, we will use the tangent trigonometric function.
Tangent function:
[tex]\displaystyle tan\theta=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
Subsiute given side lengths:
[tex]\displaystyle tan\theta=\frac{25}{8}[/tex]
Divide:
[tex]\displaystyle tan\theta=3.125[/tex]
Take the inverse tangent of both sides of the equation to solve for θ:
[tex]\displaystyle tan^{-1}(tan\theta)= tan^{-1}(3.125)[/tex]
Simplify:
[tex]\displaystyle \theta=72.2553284 \°[/tex]
Round to the nearest degree:
[tex]\displaystyle \theta=72 \°[/tex]
