According to OSHA, a ladder that is placed against a wall should make a 75.5 degree angle with the ground for optimal safety. To the nearest tenth of a foot, what is the maximum height that a 10-ft ladder can safely reach?(trigonometry)
Hypotenuse equals 10
Angle from ground to ladder: 75.5 degree
Height 9.7
what is 10*sin75.5deg ?
9.7ft
To find the maximum height that a 10-ft ladder can safely reach when placed against a wall at a 75.5-degree angle, you can use the trigonometric function of sine.
The sine function relates the angle of elevation (θ) to the opposite side (height) and the hypotenuse (the length of the ladder). In this case, the opposite side is the height, and the hypotenuse is the 10-ft ladder.
sine(θ) = height / hypotenuse
Rearranging the formula, we have:
height = sine(θ) * hypotenuse
Substituting the values given:
height = sine(75.5°) * 10 ft
Now, let's calculate the maximum height using a scientific calculator or online calculator:
height ≈ 9.8 ft (rounded to the nearest tenth of a foot)
Therefore, the maximum height that a 10-ft ladder can safely reach when placed against a wall at a 75.5-degree angle is approximately 9.8 feet.