Question

Plz help will mark right answers brainliest!!

Answer 1

Answer:

The angle between the ladder and the wall is of approximately 32 degrees $(32^o)$, 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 $\theta$ 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 $\theta$ , 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 $\theta$  which is defined as the quotient between the opposite side divided the adjacent side to investigate  the measure of the angle $\theta$ . We will use the "arctangent" to solve for the angle:

$tan(\theta)= \frac{opposite}{adjacent} \\tan(\theta)= \frac{5}{8}\\tan(\theta)=0.625\\\theta=arctan(0.625)\\\\\theta=32.00538$

which can be rounded to $32^o$