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 Algebra
 law of sine
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effort
Senior Member

USA
38 Posts

Posted - 11/09/2011 :  10:13:46  Show Profile  Reply with Quote
A baseball fan is sitting directly behind home plate in the last row of the upper deck of Comiskey park in Chicago. The angle of depression to home plate is 2954' and the angle of depression to the pitcher's mound is 2412'. In major league baseball, the distance between home plate and the pitcher's mound is 60.5ft. How far is the fan from home plate?
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the_hill1962
Advanced Member

USA
1468 Posts

Posted - 11/09/2011 :  10:45:57  Show Profile  Reply with Quote
You put the title of the post "Law of Sine" so obviously you would use The Law of Sine to do the problem.
Yes, this is not a "one step" problem where you just stick numbers into the formula. However, we need to know what you have done to try to solve the problem. Have you drawn a diagram? If so, there are some angles that you need to do some simple arithmetic on to get the measures to put into the formula. Do you even know how to use The Law of Sines?
You see, if you read the posting rules, you will see that we don't just answer problems for you. You need to tell us at least how to start the problem or what you don't understand about it.
If you don't know what The Law of Sine is, then we can explain it. If you don't understand how to draw a diagram or what "angle of depression is", we can explain it...
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effort
Senior Member

USA
38 Posts

Posted - 11/09/2011 :  12:03:25  Show Profile  Reply with Quote
I know that the definition of the angle of depression is angle between the line of sight and the horizontal when an obsever looks upward. I know that the law of sine is (sinA/a) = (sinB/b)= (sinC/c)

I know I could solve this problem if I had a correct picture diagram. I did draw a picture but I drew a diagram but I don't know where to put the given numbers. I drew a basic diamond resulting a baseball field and labeled the 1st base A, 2nd base B and 3rd base C. I don't know where to go from here.
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effort
Senior Member

USA
38 Posts

Posted - 11/09/2011 :  13:37:40  Show Profile  Reply with Quote
I say is 2954' - 2412' which = 542'

so using law of sine (b/sin 2412') = (60.5/sin 542')

b = (60.5sin2412')/(sin542')

b = 249.7

So the fan is 249.7 feet from home plate. Is this correct?
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the_hill1962
Advanced Member

USA
1468 Posts

Posted - 11/09/2011 :  14:59:09  Show Profile  Reply with Quote
Your answer is correct!
You shouldn't need to be drawing the diamond with the bases. What you need to be doing is drawing the profile that shows the angles.
Here is a sketch where *=the person in stands, P is pitcher's mound and H is home plate.

---------------------------------------------*
............................2412'........+...../
.................................+.............../
......................+......................../
...............P.............................H
..............................60.5

The ++++++ line is the distance from the person to the pitcher's plate and the / line is the distance from the person to the home plate.
The .... line is the distance from home plate to the pitcher's mound

The problem is asking you to get the distance from the person to the home plate. That is / line.
Here is that triangle drawn separately:
.....................................................542'
......................................................*
.........................................+........./
.................................+.............../ ..x
......................+......................../
...............P.............................H
..............................60.5

Now, you may be asking how to set up the ratios.
Hopefully you see that you can make

sin (542')...........sin(P)
---------.......=......-------
60.5........................x

The abovoe "(P)" is referring to the angle from the pitcher's mound looking up to the person in the stand. The "x" is reffering to the answer to the problem (the distance from home up to the person).
Now, you may wonder what is the measure of angle P?
Well, it would just be 2412' since you have alternate interior angles of a transversal between parallel lines.

Hopefully this all makes sense and my diagram is understandable. If you have any questions, please reply.

Edited by - the_hill1962 on 11/09/2011 16:11:59
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effort
Senior Member

USA
38 Posts

Posted - 11/15/2011 :  13:25:08  Show Profile  Reply with Quote
Thank you for the diagram. Although I was able to figure out the correct answer using my diagram, I think I was definitely overthinking the diagram. Your diagram was perfect.
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