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Math Help - Trig Word Problem Help!

  1. #1
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    Trig Word Problem Help!

    I need help with this word problem:
    If you stand in shallow water and look at an object below the surface of the water, the object will look farther away from you than it really is. This is because when light rays pass between air and water, the water refracts, or bends, the light rays. The index of refraction for water is 1.333. This is ratio of the sine of theta1 and the sine of theta2
    a)You are standing in water that is 2 feet deep and are looking at a rock at angle
    theta1 =60 degrees(measurement from a line perpendicular to the surface of the water). Find theta2.
    b)Find the distance x and y
    c)Find the distance d between where the rock is and where it appears to be.
    d)What happens to d as you move closer to the rock? Explain you reasoning.

    Here's a picture to help:
    Attached Thumbnails Attached Thumbnails Trig Word Problem Help!-water-problem.png  
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  2. #2
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    Re: Trig Word Problem Help!

    Did you try to answer the question yet? Maybe posting your attempted solution will help.
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  3. #3
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    Re: Trig Word Problem Help!

    For (a): According to the information provided, (sine theta1)/(sine theta2)=1.333. theta1 has been given as 60 degrees. Therefore, (sine 60)/(sine theta2)=1.333, and theta2 is easy to find. Therefore, theta2=40.5176 degrees. (Rounded off to nearest 4th decimal place)

    Fr (b): For x, since from (a), you know theta2, and because the triangle between the floor, the perpendicular line, and the line from the surface of the water (where the perpendicular line cuts) to the object is a right angle triangle, it is easily found as well. Let's say the third angle is theta3, then it would be 90 degrees-theta2, and using the Law of Sines, x/sine theta2=2ft/sine theta3. Therefore, theta3=49.4824 degrees, which means that x=1.7092. If I remember my physics lesson correctly, the angle between the perpendicular line and the illusion of the rock is the same as theta1, which I will call theta4, to avoid confusion. So, theta4=theta1=60 degrees. Therefore, theta5, which is the angle at the illusion of the rock, would be 30 degrees. Using the Law of Sines again, y/sine theta4=2ft/sine theta5. Therefore, y=3.4641.

    For (c): d is the difference between x and y, therefore y-x=3.4641-1.7092=1.7549.

    For (d): Easily reasonable.

    I hope these help.
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  4. #4
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    Re: Trig Word Problem Help!

    Quote Originally Posted by rk14 View Post
    I need help with this word problem:
    If you stand in shallow water and look at an object below the surface of the water, the object will look farther away from you than it really is. This is because when light rays pass between air and water, the water refracts, or bends, the light rays. The index of refraction for water is 1.333. This is ratio of the sine of theta1 and the sine of theta2
    a)You are standing in water that is 2 feet deep and are looking at a rock at angle
    theta1 =60 degrees(measurement from a line perpendicular to the surface of the water). Find theta2.
    b)Find the distance x and y
    c)Find the distance d between where the rock is and where it appears to be.
    d)What happens to d as you move closer to the rock? Explain you reasoning.

    Here's a picture to help:
    The book you reproduced the question from and the image too is mistaken. The object will look closer to you.

    Trig Word Problem Help!-untitled2.gif

    Are using this book at school or you purchased the book online
    Thanks from LimpSpider
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  5. #5
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    Re: Trig Word Problem Help!

    Quote Originally Posted by votan View Post
    The book you reproduced the question from and the image too is mistaken. The object will look closer to you.

    Click image for larger version. 

Name:	untitled2.gif 
Views:	6 
Size:	8.6 KB 
ID:	29465

    Are using this book at school or you purchased the book online
    And I totally forgot that...

    This means that my answers to the OP's questions are wrong. :P
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