Hi I with a displacement type problem

[Haniszmi]

Homework Statement

In a mall, a shopper rides up an escalator between floors. At the top of the escalator, the shopper turns right and walks 9 meters to a store. The magnitude of the shopper's displacement from the bottom of the escalator is 16m. The vertical distance between the floors is 6m. At what angle is the escalator inclined above the horizontal?

Homework Equations

Pythagorean theorem/ soh cah toa

The Attempt at a Solution

I had a hard time visualizing this problem. I drew my first triangle as if I was standing in front of the escalator, which was a straight line x going north, then my next leg 9m long eastward and my hypotenuse 16m long diagonal. I did not get the correct answer of 27 degrees. I drew my second triangle as if i was watching the escalator from the side and all I had was one leg which was the height of 6m being the distance between the ceiling and the floor. Someone help me solve this please.

 

[Mentallic]

Well you were on the right track. You just needed to combine those two triangles so your last triangle with the 6m height had its hypotenuse as well (which is the escalator distance you found from using pythagoras' theorem on the other triangle) and you can use your trig from there.

If you can't visualize the scenario, make a sketch of it on paper and include all angles and sides you know and the ones you find. You will notice it is only a 2-step problem.

 

[baba89]

Hello,

Thank you for reaching out for help with this problem. It sounds like you are on the right track by using the Pythagorean theorem and trigonometric functions to solve this problem. However, it seems that you may be visualizing the situation incorrectly.

To correctly visualize the problem, imagine that you are looking at the escalator from the side, as you mentioned. Now, draw a right triangle where the vertical leg is 6m (the distance between the floors), the horizontal leg is 9m (the distance to the store), and the hypotenuse is the total displacement of 16m. This will form a right triangle where the angle between the 6m and 16m sides is the angle of inclination of the escalator.

Using the Pythagorean theorem, we can solve for the length of the hypotenuse (16m). Then, using trigonometric functions, we can solve for the angle of inclination. Remember to use the inverse trigonometric functions (arcsin, arccos, arctan) to find the angle.

I hope this helps and good luck with your problem solving!