Elton is using a ladder that is 20 feet long to reach a spot on a wall that is 16 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.(1 point)
To determine if Elton is within the allowed angle measures, we need to find the angle formed at the base of the ladder.
Let x be the angle formed at the base of the ladder. We can use the tangent function:
tan(x) = opposite / adjacent
tan(x) = 16 / 20
tan(x) = 0.8
Now, we use the inverse tangent (or arctan) to find the angle:
x = arctan(0.8)
x ≈ 38.6 degrees
Since the angle formed at the base of the ladder is 38.6 degrees, Elton is within the allowed angle measures as 72° < 38.6° < 78°.