Avery leans a 24-foot ladder against a wall so that it forms an angle of 80degrees
∘
with the ground. How high up the wall does the ladder reach? Round your answer to the nearest tenth of a foot if necessary.
To find the height up the wall that the ladder reaches, we can use trigonometry. The height of the wall can be represented as the opposite side of the right triangle formed by the ladder against the wall, with the ladder acting as the hypotenuse.
We know the length of the ladder (hypotenuse) is 24 feet, and the angle formed with the ground is 80 degrees. We want to find the height up the wall (opposite side).
Using the sine function:
sin(80°) = opposite / hypotenuse
sin(80°) = h / 24
To solve for h, we can rearrange the equation:
h = 24 * sin(80°)
h ≈ 23.4 feet
Therefore, the ladder reaches approximately 23.4 feet up the wall.