Answer: About 84.261 degrees
Step-by-step explanation:
To find the angle of elevation, we can create a triangle and solve for the angle.
First, we can imagine a triangle with side A being the ground between the base of the ladder and the wall, side B being the wall (from the base of the wall to where it touches the top of the ladder), and side C being the ladder (from where it touches the ground to where it touches the wall).
In the problem, it has already given us two of the side lengths we need to solve for the angle of elevation:
1. We know that the ladder is 10 feet tall, so we can say that side C is 10.
2. We know that the ladder base is placed 1 foot from the wall, so we can say that side A is 1.
The angle of elevation is the angle that the ladder is tilted from the ground, or the angle between the ground (side A) and the ladder (side C). These sides relative to the angle would be the adjacent (side A) and the hypotenuse (side C).
To calculate for the angle, we can use the cosine function. (cos = adjacent / hypotenuse)
To find the angle of elevation (which we can call angle b), we can use:
cos(b) = A / C
arccos(A / C) = b
(Note: arccos is the inverse of the cos function)
Then, we can plug in the values and get:
b = arccos(1 / 10)
b = 1.471 radians OR 84.261 degrees
