The proper angle for a ladder is about 75 degrees from the ground. Suppose you have a 23 foot
ladder. How far from the house should you place the base of the ladder? Round to the hundredths..
(2 decimal places)
Using trigonometry, we can use the sine function to solve for the distance from the base of the ladder to the house:
sin(75 degrees) = opposite/hypotenuse
We know the hypotenuse (ladder) is 23 feet, so we can solve for the opposite (distance from house):
sin(75 degrees) = opposite/23
opposite = 23*sin(75 degrees)
opposite = 22.36 feet
Rounded to the nearest hundredths, the distance from the house should be 22.36 feet.
The bot found how far up the wall the ladder is placed.
That was not the question
I apologize for the mistake. To find how far from the house the base of the ladder should be placed, we can use the cosine function:
cos(75 degrees) = adjacent/hypotenuse
We know the hypotenuse (ladder) is 23 feet, so we can solve for the adjacent (distance from house):
cos(75 degrees) = adjacent/23
adjacent = 23*cos(75 degrees)
adjacent = 5.84 feet
Rounded to the nearest hundredths, the distance from the house should be 5.84 feet.
To find the distance from the house, we can use trigonometry.
The ladder forms a right triangle with the ground and the wall, with the ladder being the hypotenuse of the triangle.
We can use the cosine function to find the distance from the house. The cosine function relates the adjacent side (distance from the house) to the hypotenuse (length of the ladder).
cos(angle) = adjacent/hypotenuse
cos(75 degrees) = adjacent/23 feet
To find the adjacent side:
adjacent = cos(75 degrees) * 23 feet
Using a calculator, cos(75 degrees) is approximately 0.2588.
adjacent = 0.2588 * 23 feet
adjacent is approximately 5.9524 feet.
Therefore, you should place the base of the ladder approximately 5.95 feet from the house.