To find how far up the wall the ladder reaches, we can use trigonometry. The ladder forms a right triangle with the wall, where the ladder is the hypotenuse and the distance up the wall is the opposite side.
Let's label the sides of the triangle:
- The hypotenuse (ladder) is 15 ft.
- The angle between the ladder and the wall is 40°.
To find the distance up the wall (opposite side), we can use the sine function, which is defined as the ratio of the length of the opposite side to the length of the hypotenuse
The equation we can use is: sin(angle) = opposite/hypotenuse
Substituting the values:
sin(40°) = opposite/15 ft
To find the opposite side, we can rearrange the equation:
opposite = sin(40°) * 15 ft
Calculating the value:
opposite = 0.64279 * 15 ft
opposite ≈ 9.6 ft (rounded to the nearest tenth)
Therefore, the ladder reaches approximately 9.6 ft up the wall.