Answer:
θ=arctan(6/5)
Step-by-step explanation:
To determine if the ladder will be unstable, we need to calculate the angle the ladder makes with the ground when it's placed against the wall to reach a window that is 10 feet above the ground. We can use trigonometry to find this angle.
Let's define:
ℎ
h as the height of the window above the ground, which is 10 feet.
ℓ
ℓ as the length of the ladder, which is 12 feet.
The angle
θ that the ladder makes with the ground can be found using the tangent function:
tan
(
)
=
ℎ
ℓ
tan(θ)=
ℓ
h
Substitute the values:
tan
(
)
=
10
ft
12
ft
tan(θ)=
12ft
10ft
tan
(
)
=
5
6
tan(θ)=
6
5
Now, find the angle
θ by taking the inverse tangent (arctan) of
5
6
6
5
: