A ladder 8.70 m long leans against the side of a building. If the ladder is inclined at an angle of 69.0° to the horizontal, what is the horizontal distance from the bottom of the ladder to the building?
cos 69 = h/8.7
Odd question for physics, this is Alg II or very basic trig.
Length=8.70*cos69
To find the horizontal distance from the bottom of the ladder to the building, we can use trigonometry.
We have the length of the ladder (8.70 m) and the angle it makes with the horizontal (69.0°).
Let's consider the right triangle formed by the ladder, the horizontal distance, and the height of the building. The ladder is the hypotenuse of the triangle, the horizontal distance is the adjacent side, and the height of the building is the opposite side.
We can use the cosine function, which relates the adjacent side and the hypotenuse:
cos(angle) = adjacent/hypotenuse
In this case, the adjacent side is the horizontal distance, the angle is 69.0°, and the hypotenuse is the length of the ladder. Let's substitute these values into the equation:
cos(69.0°) = horizontal distance/8.70 m
To find the horizontal distance, we can rearrange the equation:
horizontal distance = cos(69.0°) * 8.70 m
Now, let's calculate the value of cos(69.0°) using a calculator or a math software:
cos(69.0°) ≈ 0.3473
Now, substitute this value into the equation:
horizontal distance ≈ 0.3473 * 8.70 m
horizontal distance ≈ 3.02 m
Therefore, the horizontal distance from the bottom of the ladder to the building is approximately 3.02 meters.