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A student stands do = 2.1 m in front of a floor-to-ceiling mirror. Her eyes are he = 1.47 m above the floor and she holds a flashlight at a distance hp= 0.75 m above the floor. Randomized Variables do 2.1 m he 1.47 m h 0.75 m Calculate the angle 0, in degrees, that the flashlight makes with respect to the floor if the light is reflected into her eyes. Grade Su Deduction Potential

Respuesta :

Answer:

[tex]\angle r=9.7276^{\circ}=\angle i[/tex]

Explanation:

Given:

  • distance between the student and the mirror, [tex]d_o=2.1\ m[/tex]
  • height of the eyes from the ground, [tex]h_e=1.47\ m[/tex]
  • height of the torch above the ground, [tex]h_p=0.75\ m[/tex]

Refer the schematic for the clarity of the situation and geometrical interpretation.

Distance between the eyes and the torch:

[tex]\Delta h=h_e-h_p[/tex]

[tex]\Delta h=1.47-0.75[/tex]

[tex]\Delta h=0.72\ m[/tex]

Now, as we know the law of reflection that angle of incident is equal to the angle of reflection:

We take the triangle NBT:

[tex]EB=BT=0.36\ m[/tex]

Now the angle r:

[tex]\tan r=\frac{BT}{BN}[/tex]

[tex]\tan r=\frac{0.36}{2.1}[/tex]

[tex]\angle r=9.7276^{\circ}=\angle i[/tex]

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