Explanation:
We can use trigonometry to find the measure of the angle that the ladder forms with the ground.
Let θ be the angle that the ladder makes with the ground. Then, we can use the tangent function to relate the opposite side (the height of the window, 10.5 feet) to the adjacent side (the distance from the base of the ladder to the wall):
tan(θ) = opposite / adjacent
tan(θ) = 10.5 / x
where x is the distance from the base of the ladder to the wall.
We can solve for x by using the Pythagorean theorem, which relates the sides of a right triangle:
x^2 + 10.5^2 = 12^2
x^2 = 144 - 10.5^2
x^2 = 42.25
x = √42.25
x ≈ 6.5
Substituting this value into the equation for tangent, we get:
tan(θ) = 10.5 / 6.5
tan(θ) ≈ 1.6154
To find θ, we can take the inverse tangent (or arctangent) of both sides:
θ = tan^-1(1.6154)
θ ≈ 58.27°
Therefore, the measure of the angle that the ladder forms with the ground, to the nearest degree, is 58°.