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November 26th, 2008, 03:58 PM   #1
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Quick high school math question...

? and ? are acute angles in quadrant I, with sin ? = 7/25 and cos B = 5/13. Determine the value of sin (? + ?)

The answer is 323 / 325

I started with
sin (? + ?) = sin ? cos ? + cos ? sin ?
? = 7/25
B = 5/13
sin (7/25) cos (5/13) + cos (7/25) sin (5/13)
...but, where do you go from there?
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November 26th, 2008, 05:22 PM   #2
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Re: Quick high school math question...

Quote:
Originally Posted by lanvin12
? and ? are acute angles in quadrant I, with sin ? = 7/25 and cos B = 5/13
? = 7/25
B = 5/13
a = sin^-1(7/25)

B = cos^-1(5/13)

sin(a + B) = 323/325
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November 27th, 2008, 05:47 PM   #3
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Re: Quick high school math question...

Quote:
Originally Posted by lanvin12
[b]? and ? are acute angles in quadrant I, with [color=#FF0000]sin ?[/color] = 7/25
...
I started with
...
[color=#FF0000]?[/color] = 7/25
There is a difference, do you think?

You have sin (? + ?) = sin ? cos ? + cos ? sin ?
You know sin a, so you need from that cos a.
You know cos B, so you need from that sin B.

Draw right triangle for each case separately, one containing angle a, and one containing angle B, and label sides from the given ratios. Find the third side using Pythagoras, and then find the missing trig functions.

Dave.
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