A heavy piece of machinery is raised by sliding its 12.5 m along a plank oriented at 20 degrees to the horizontal.
How high above its original position is it raised?
How far is it moved horizontally?
Can you please give me the formulas for these? Thank you very much!
The distance of 12.5 m is measureed along the plank, so 12.5 m is the hypotenuse. So
rise=12.5*sin(20°)
To vanessa, why would it be tan, when the 12.5 is the hypotenuse because the way you formulated is saying that 12.5 is x.
Sure! To answer these questions, we can use trigonometry and some basic physics principles.
1. The height above its original position (vertical displacement) can be calculated using the formula: vertical displacement = distance * sin(angle). In this case, the distance is 12.5 m and the angle is 20 degrees. So, the height above its original position would be: vertical displacement = 12.5 m * sin(20 degrees).
2. To determine the horizontal distance, you can use the formula: horizontal displacement = distance * cos(angle). Again, in this case, the distance is 12.5 m and the angle is 20 degrees. So, the horizontal distance would be: horizontal displacement = 12.5 m * cos(20 degrees).
By plugging these values into these formulas, you'll be able to find the answers.
tan 20(degrees)=Opposite/Adjacent
=O/12.5
12.5tan20(degrees)=O
O=horizontal