A ladder is leaning against a wall. The base of the ladder is 8 feet from the wall, and the top of the ladder is at a height of 10 feet. What is the angle from the ground to the top of the ladder? Round your answer to the nearest degree.
To find the angle from the ground to the top of the ladder, we can use the inverse tangent function. The inverse tangent of the height of the ladder divided by the distance from the wall gives us the angle in radians. We can then convert this angle from radians to degrees.
Let's call the angle from the ground to the top of the ladder θ.
Using the inverse tangent function, we have:
θ = arctan(height/distance)
θ = arctan(10/8)
θ ≈ arctan(1.25)
Using a calculator, we find that arctan(1.25) ≈ 51.34 radians.
To convert this angle from radians to degrees, we multiply by 180/π:
θ ≈ 51.34 × 180/π
θ ≈ 2946.8/π
θ ≈ 937.3 degrees
Rounded to the nearest degree, the angle from the ground to the top of the ladder is approximately 937 degrees.