How to solve for angle of reflection in respect to floor?

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SUMMARY

The discussion focuses on calculating the angle of reflection for a flashlight held by a student in front of a floor-to-ceiling mirror. The student is positioned 2.7 meters from the mirror, with her eyes 1.64 meters above the floor and the flashlight 0.85 meters above the floor. Participants emphasize the importance of accurately drawing the geometry of the problem to align with the given dimensions and clarify the angles involved. The use of inverse tangent to find the angle is suggested, but participants highlight the need for precise setup and understanding of the triangles formed by the light's reflection.

PREREQUISITES
  • Understanding of basic trigonometry, specifically tangent and sine functions.
  • Ability to interpret geometric diagrams and apply them to real-world problems.
  • Familiarity with the concept of angles of incidence and reflection.
  • Basic knowledge of how to set up and solve problems involving right triangles.
NEXT STEPS
  • Study the properties of angles of incidence and reflection in optics.
  • Learn how to accurately draw and label geometric diagrams for physics problems.
  • Practice solving problems involving inverse tangent and right triangles.
  • Explore applications of trigonometry in real-world scenarios, such as light reflection and refraction.
USEFUL FOR

This discussion is beneficial for students studying physics, particularly those tackling problems related to optics and geometry, as well as educators seeking to enhance their teaching methods in these areas.

AngelLegs
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Homework Statement


A student stands 2.7 m in front of a floor-to-ceiling mirror. Her eyes are 1.64 m above the floor and she holds a flashlight at a distance 0.85 m above he floor.
Calculate the angle θ, in degrees, that the flashlight makes with respect to the floor if the light is reflected into her eyes.

Homework Equations


tangent
sine

The Attempt at a Solution


I'll use inverse tangent (1.64m/2.7m) to find the angle, but I'm not sure how to set it up. I'm confused about which angle I'm finding when I use that, and which "triangle" I'm supposed to be solving for, because the light ray makes a triangle when it reflects off the mirror, and the light makes another when it reflects into the students eyes. But I'm having huge complications with figuring which ones to apply to the problem solving process.
 
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Draw a diagram. Also, please don't use HUGE bold print. It's unnecessary and some of us view it as obnoxious, like screaming your question.
 
phinds said:
Draw a diagram. Also, please don't use HUGE bold print. It's unnecessary and some of us view it as obnoxious, like screaming your question.
I'm sorry, I'm new
I don't quite know how to use this website yet
Can you see the photo I posted?
 

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Yes. I think you have errors in your drawing in that not everything conforms to your problem statement. Another issue is that you don't know the distance of the light from the torso, so you must assume it to be zero (light is being held by side, not out front).

Get the drawing to exactly conform to the problem statement and you then have everything needed to solve this trivial problem.
 
phinds said:
Yes. I think you have errors in your drawing in that not everything conforms to your problem statement. Another issue is that you don't know the distance of the light from the torso, so you must assume it to be zero (light is being held by side, not out front).

Get the drawing to exactly conform to the problem statement and you then have everything needed to solve this trivial problem.
I'm afraid I'm not understanding what you mean.
Is it like this?
 

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You're getting the idea. I know you have the right idea but do you really think this is an accurate model of the problem? Why does the light not line up with the stated distance. Stop drawing a stick figure and just draw the geometry.
 

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