Answer:
The angle between the ladder and the wall is of approximately 32 degrees [tex](32^o)[/tex], which agrees with the answer marked as "B" in the list of options.
Step-by-step explanation:
Notice that the wall and the floor make a right angle, and the ladder lining against the wall makes the hypotenuse of a right angle triangle.
See the attached image for explanation, and for the angle [tex]\theta[/tex] that we are trying to find, which is formed between the ladder and the wall.
Notice as well that the 8 ft section of the wall, is an "adjacent" side of the angle [tex]\theta[/tex] , and that the 5 ft segment between the wall and the base of the ladder is the "opposite" side to the angle.
We can then use the "tangent" of the angle [tex]\theta[/tex] which is defined as the quotient between the opposite side divided the adjacent side to investigate the measure of the angle [tex]\theta[/tex] . We will use the "arctangent" to solve for the angle:
[tex]tan(\theta)= \frac{opposite}{adjacent} \\tan(\theta)= \frac{5}{8}\\tan(\theta)=0.625\\\theta=arctan(0.625)\\\\\theta=32.00538[/tex]
which can be rounded to [tex]32^o[/tex]
