A 32-foot ladder leans against a building on level ground. It just reaches a window 25 feet above
the ground. To the nearest degree, what angle does the ladder make with the ground.
just find θ where
sinθ = 25/32
To find the angle that the ladder makes with the ground, we can use the trigonometric function known as the inverse tangent (arctan). The inverse tangent of the ratio of the height of the building to the distance from the base of the ladder to the building will give us the angle.
In this case, the height of the building is 25 feet and the distance from the base of the ladder to the building is 32 feet. Therefore, we can calculate the angle as follows:
Angle = arctan(height / distance)
Angle = arctan(25 / 32)
To find the value of this expression, we can use a scientific calculator or an online calculator with the arctan (or tan^(-1)) function.
After calculating the expression, the angle is approximately 38.83 degrees. Rounded to the nearest degree, the angle that the ladder makes with the ground is 39 degrees.