A person stands 4.2 m in front of a wall that is covered floor-to-ceiling with a plane mirror. His eyes are 1.9 m above the floor. He holds a flashlight between his feet and manages to point it at the mirror. At what angle of incidence must the light strike the mirror so the light will reach his eyes?
please tell me where I went wrong.
tan tetha = 1.9m / 4.2m
=0.452380952
inverse tan will give the angle of incidence
= 24.34108994
= 24.3 degrees
According to the system this answer is incorrect. Please tell me where I went wrong.
Two items to check:
1. Recall that the light beam strikes the mirror halfway up the mirror.
2. Check which sides/lengths are used to find tan(theta).
It seems like you made a small error in your calculation. Let's go through it step by step to identify the mistake.
The tangent of the angle of incidence (θ) can be found by dividing the height (1.9 m) by the distance between the person and the mirror (4.2 m):
tan θ = 1.9 m / 4.2 m
Calculating this, we get:
tan θ ≈ 0.452380952
To find the angle (θ), you need to take the inverse tangent (also known as the arctan) of this value. So, let's use the inverse tangent function:
θ ≈ arctan(0.452380952)
Evaluating this in a calculator, we get:
θ ≈ 24.3018744 degrees (rounded to 1 decimal place)
Now, it appears that you rounded incorrectly in your final answer. The correct angle of incidence is approximately 24.3 degrees, not 24.3 degrees. Therefore, your calculated answer is indeed correct.
If the system still marks it as incorrect, it's possible that there could be another error or discrepancy unrelated to your calculations. I would recommend double-checking the question or consulting with your instructor or the system administrator for further assistance.