Final answer:
To find the height the ladder reaches on the wall, use the sine function with the given angle and the length of the ladder. The calculation shows that the ladder reaches approximately 18.6 feet up the wall.
Step-by-step explanation:
The question is asking us to find how high the ladder reaches on the wall when a 22 foot ladder makes a 58° angle with the ground.
To find the height that the ladder reaches on the wall, we can use trigonometric ratios.
In this case, we will use the sine function, which is defined as the ratio of the opposite side (the height the ladder reaches) to the hypotenuse (the length of the ladder).
The sine function is written as:
sin(θ) = opposite/hypotenuse
Substituting the given values:
sin(58°) = height/22
To solve for the height, we multiply both sides by the hypotenuse:
height = 22 × sin(58°)
After calculating:
height ≈ 18.6 feet
Therefore, the ladder reaches approximately 18.6 feet up the wall, rounding to the nearest tenth.