A ladder 8.65 m long leans against the side of a building. If the ladder is inclined at an angle of 63.0° to the horizontal, what is the horizontal distance from the bottom of the ladder to the building?
8.65 cos 65 = 3.66 m
To find the horizontal distance from the bottom of the ladder to the building, we can use trigonometry and the given information.
Let's break the problem down:
Given:
- Length of the ladder (hypotenuse): 8.65 m
- Angle of inclination (θ): 63.0°
We need to find:
- Horizontal distance (adjacent side): ?
Using trigonometric functions, we can determine the horizontal distance by using the cosine function, which relates the adjacent side to the hypotenuse and the angle.
cos(θ) = adjacent / hypotenuse
Substituting the values we have:
cos(63.0°) = adjacent / 8.65 m
To isolate the adjacent side, we can rearrange the equation:
adjacent = cos(63.0°) * 8.65 m
Now, let's calculate the answer:
adjacent = cos(63.0°) * 8.65 m
adjacent ≈ 3.592 m
Therefore, the horizontal distance from the bottom of the ladder to the building is approximately 3.592 m.