How high does an 8-foot ladder reach on a wall when it makes a 55° angle with the ground?

To determine how high an 8-foot ladder reaches on a wall when it makes a 55° angle with the ground, we can use the concept of right triangles and trigonometry, specifically the sine function which relates the angle, the opposite side (the height reached on the wall), and the hypotenuse (the length of the ladder).

In this scenario:

• The hypotenuse is the length of the ladder, which is 8 feet.

• The angle with the ground is 55°.

• The side opposite the angle is the height reached on the wall, which we want to calculate.

Using the sine function:

[

\text{sine(angle)} = \frac{\text{opposite}}{\text{hypotenuse}}

]

We can rearrange this to solve for the height (the opposite side):

[

\text{height} = \text{hypotenuse} \times \sin(\text{angle})

]

Substituting the known values:

[

\text{height} = 8 \times \sin(55°)

]

Using a calculator to find (\sin(55°) \approx 0.8192):

[

\text{height}