The use of a ladder is considered safe if the angle between the ground and the ladder is less than 75°. Charlie’s 5 ft long ladder is 1 ft from the base of a wall.a.) Is the ladder being used safely? b.)How far away from the wall is the minimum distance Charlie’s other ladder should be if it is 10 ft long?
4 years ago
Answered By Mohammed B
Part a.The ladder is 5ft long, which is the hypotenuse since ladders are oriented diagonally. 1ft from the wall is the horizontal since it is telling us the distance the ladder is from the wall's base. If you remember trigonometry, you have three functions: sine, cosine,and tangent. Remember the acronym SOHCAHTOA (Sine:Opposite/Hypotenuse, Cosine: Adjacent/Hypotenuse Tangent: Opposite/Adjacent) Since we are given the length of the triangle drawn below TOUCHING the angle we are given the adjacent length of 1ft. And the hypotenuse (longest length of a right triangle) is 5ft. So use
arccos(1ft/5t)=angle and MAKE SURE your calculator is set to degree mode.
The angle is 78.4 degrees. This is greater than 75 degrees so NO THE LADDER IS NOT BEING USED SAFELY!
As for partb. I am not fully certain of the grammar but I am assuming that it is asking the minimum distance from the wall if the ladder is 10ft. If that is the case, then the ladder (diagonal) is 10ft long, we are looking for the adjacent side (touching the angle) since it is asking the distance the ladder's base is from the wall's base (marked as the variable x). And the angle (theta) is 75 degrees since that is the maximum angle for the ladder to be safe.
Use cos(theta)=adjacent/hypotenuse
cos(75)=x/10
10*cos(75)=x
x=2.59ft
Hope this helps.
4 years ago
Answered By Jackie C
a) For the 5 ft ladder, the min distance from the should be
5*COS(75 degree)=1.29 ft, therefore, the 1 ft distance is not safe
b) Min distance from the wall for a 10 ft ladder is
4 years ago
Answered By Mohammed B
Part a.The ladder is 5ft long, which is the hypotenuse since ladders are oriented diagonally. 1ft from the wall is the horizontal since it is telling us the distance the ladder is from the wall's base. If you remember trigonometry, you have three functions: sine, cosine,and tangent. Remember the acronym SOHCAHTOA (Sine:Opposite/Hypotenuse, Cosine: Adjacent/Hypotenuse Tangent: Opposite/Adjacent) Since we are given the length of the triangle drawn below TOUCHING the angle we are given the adjacent length of 1ft. And the hypotenuse (longest length of a right triangle) is 5ft. So use
arccos(1ft/5t)=angle and MAKE SURE your calculator is set to degree mode.
The angle is 78.4 degrees. This is greater than 75 degrees so NO THE LADDER IS NOT BEING USED SAFELY!
As for partb. I am not fully certain of the grammar but I am assuming that it is asking the minimum distance from the wall if the ladder is 10ft. If that is the case, then the ladder (diagonal) is 10ft long, we are looking for the adjacent side (touching the angle) since it is asking the distance the ladder's base is from the wall's base (marked as the variable x). And the angle (theta) is 75 degrees since that is the maximum angle for the ladder to be safe.
Use cos(theta)=adjacent/hypotenuse
cos(75)=x/10
10*cos(75)=x
x=2.59ft
Hope this helps.
4 years ago
Answered By Jackie C
a) For the 5 ft ladder, the min distance from the should be
5*COS(75 degree)=1.29 ft, therefore, the 1 ft distance is not safe
b) Min distance from the wall for a 10 ft ladder is
10*COS(75 degree)=2*1.29=2.58 ft