A 10 foot ladder is to be placed against the wall, the base of the ladder must be placed at an angle of 72 degrees with the level ground for secure footing find to the nearest in how far the base of the ladder should be from the wall the ladder will reach?
base distance= 10 cos72
height on wall= 10 sin72
To find the distance the base of the ladder should be from the wall, we can use the trigonometric functions sine and cosine.
Given that the ladder is 10 feet long and the angle between the ladder and the ground is 72 degrees, we can use the cosine function to find the base distance of the ladder from the wall.
The cosine function is defined as the adjacent side divided by the hypotenuse in a right triangle. In this case, the adjacent side is the base distance we are trying to find, and the hypotenuse is the length of the ladder, which is 10 feet.
So, the formula to find the base distance is:
base distance = ladder length * cosine(angle)
Substituting the values we have, we get:
base distance = 10 * cos(72)
Using a calculator, we can evaluate this expression to find the base distance. Rounding the result to the nearest whole number, we find that the base distance should be approximately 3.42 feet.
To find the height on the wall that the ladder will reach, we can use the sine function. The sine function is defined as the opposite side divided by the hypotenuse in a right triangle. In this case, the opposite side is the height on the wall that we are trying to find.
So, the formula to find the height on the wall is:
height on wall = ladder length * sine(angle)
Substituting the values we have, we get:
height on wall = 10 * sin(72)
Using a calculator, we can evaluate this expression to find the height on the wall. Rounding the result to the nearest whole number, we find that the ladder will reach a height of approximately 9.40 feet.