Ammarah
how do u know when to use sin and cos?
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Ammarah
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@mathstudent55
IsTim
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sin for opposite over hypotenus
cos for adjacent over hypotenus
Ammarah
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I know but like in a problem...i dont get which one i should use
Ammarah
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Use a sine or cosine ration to find the value of each variable. Round decimals to the nearest tenth.
Ammarah
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|dw:1358230193689:dw|
Ammarah
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These three please
Ammarah
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i dont get them
IsTim
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use that. sorry. i ahve to go soon.
Ammarah
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it doesnt help please solve these for me
Callisto
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|dw:1358230939592:dw|
Refer to the reference angle.
Sin => opposite side (to the reference angle) / hypotenuse
In this diagram, can you determine what sine theta is?
Ammarah
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? no
Callisto
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what is the opposite side to the reference angle theta?
Ammarah
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x
Callisto
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and what is the hypotenuse?
Ammarah
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2 btw what is theta?
Callisto
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Sorry :| that was supposed to be z :|
If you know x and z, you can find theta. Because
sin (theta) = x/z
Got it?
opiesche
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Ammara, so in an equation, Callisto is saying is that in the figure above,
\[\sin(\theta) = \frac{ x }{ z }\]
So, in your figure, the first problem: you know the hypotenuse (18) and the angle opposite x (32 degrees).
So you know that,
\[\sin(32) = \frac{ x }{ 18 }\]
Then solve for x :)
opiesche
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And that's the sine of 32 degrees of course, not radians.
Ammarah
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what do i do for why then?
Ammarah
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|dw:1358231828749:dw|
opiesche
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Well, you know that the angle opposite x is 32 degrees, and that the angle opposite the hypotentuse is 90 degrees. You also know the total sum of all interior angles of a triangle - so from that you can figure out the remaining angle you don't know, and do the same thing.
Ammarah
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i dont get it....how to i solve for y?
Ammarah
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and does x=9.5?
opiesche
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Or alternatively, use the cosine which is the adjacent angle over the hypotenuse:
\[\cos(\theta) = \frac{ y }{ z }\]
Substitute for the adjacent angle (32 degrees again) and for the hypotenuse (18), and solve for y the same way you solved for x above.
Ammarah
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|dw:1358232234127:dw|
opiesche
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Correct.
Ammarah
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Ok how about the next triangle...
Ammarah
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|dw:1358232364105:dw|
Ammarah
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|dw:1358232378783:dw|
Ammarah
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so in the left triangle were solving for a.
Ammarah
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how would u solve it? please solve it for me.......
opiesche
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Correct. And you know that the cosine of the angle (48 degrees) is the same as 10 divided by a - careful here, because a is the hypotenuse:
\[\cos(\Theta) = \frac{ 10 }{ a }\]
So,
\[\cos(48) = \frac{ 10 }{ a } \]
Ammarah
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how would i solve be now...i got 14.9 for a
opiesche
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That's correct. Now solve the last figure?
Ammarah
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b=11.1?
opiesche
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Yes!
opiesche
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You got it. Can you do the last triangle?