The Consumer Product Safety Commission recommends that the base of a ladder should be set out 1 foot from a wall for every 4 feet of vertical rise.
a. What angle will a ladder so situated make with the ground?
b. If Joe follows these recommendations, how far up the wall (vertically) will his 16 foot ladder reach?
tanØ = 4/1 = 4
Ø = 75.96
The angle should be 76°
by ratio:
4/1 = 16/x
x = 4
To find the angle the ladder makes with the ground, we can use the tangent function. The tangent of an angle is equal to the height of the ladder divided by the distance of the base from the wall. Since the height of the ladder is 16 feet and the base of the ladder is set out 1 foot for every 4 feet of vertical rise, we can calculate the distance of the base from the wall.
a. Let's first calculate the distance of the base from the wall:
For every 4 feet of vertical rise, the base should be set out 1 foot from the wall. Therefore, for a 16-foot vertical rise (height of the ladder), we can set up a proportion:
(16 ft vertical rise) / (4 ft vertical rise) = (x ft base from the wall) / (1 ft base from the wall)
4x = 16
x = 4
Therefore, the base of the ladder should be set out 4 feet from the wall.
Now we can calculate the angle the ladder makes with the ground using the tangent function:
tan(angle) = (height of the ladder) / (distance of the base from the wall)
tan(angle) = (16 ft) / (4 ft)
tan(angle) = 4
To find the angle, we can use the inverse tangent function (also known as arctan or tan^(-1)):
angle = arctan(4)
Using a calculator, we find that the angle is approximately 75.96 degrees.
b. Since Joe follows the recommendation and sets the base of the ladder 4 feet from the wall, he can extend his 16-foot ladder vertically to the wall.