Elton is using a ladder that is 24 feet long to reach a spot on a wall that is 20 feet above the ground. He places the ladder at the exact location he needs to reach. His employer uses safety measures that require the ladder to be between a 72° and 78° angle at the base of the ladder. Using the inverse of tangent, determine if Elton is within the allowed angle measures. What is the angle formed at the base of the ladder? Round your answer to the nearest whole degree.(2 points)
To determine if Elton is within the allowed angle measures, we first need to find the angle formed at the base of the ladder using the inverse tangent function.
Let x be the angle formed at the base of the ladder.
We can set up the following trigonometric equation:
tan(x) = opposite/adjacent
tan(x) = 20/24
tan(x) = 5/6
To find the angle x, we take the inverse tangent of 5/6:
x = arctan(5/6)
x ≈ 39.8056 degrees
Since the required angle measure is between 72° and 78°, we can see that Elton's angle of 39.8056° is less than the minimum allowed angle of 72°. Therefore, Elton is not within the allowed angle measures.