meg1334
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The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used.
C = 38°, a = 19, c = 10
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Hero
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Did you try simply using Law of Sines to figure it out?
meg1334
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yes but i didnt understand
Hero
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What did you come up with?
meg1334
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i got sin A = 67 but that isnt in my answer choices
No triangle is formed.
A = 58.6°, B = 83.4°, b ≈ 15.6
A = 83.4°, B = 58.6°, b ≈ 15.6
The triangle cannot be solved with the Law of Sines.
Hero
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I don't understand how you got that. Please show me the steps you took to get A = 67
meg1334
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i used c/ sin c = a/ sin a
10/sin 37 = 19/sin a
and then i divided 19 sin 38 over sin 10 and i got 67.36
Hero
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where did you get the 37 from?
meg1334
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I meant 38, i used 38 in my claculations and still got 67
meg1334
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calculations
Hero
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Are you in degree mode or radian mode?
meg1334
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i dont know i just typed it in and got 67, cant you check it?
Hero
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You must make sure you're in degree mode. That's very important.
Hero
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But either way it goes, you're not doing it correctly.
meg1334
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oh really, i hadnt noticed that im doing it wrong. I need help thats why im on here obviously
Hero
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\[\sin A = \frac{19\sin(38^{\circ})}{10}
\\\sin A =
\]
Hero
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Compute the right hand side again and let me know what you get. Make sure you're in degree mode.
meg1334
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1.169756803
Hero
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Okay now
\[\sin A = 1.169756803\]
So how do we find A?
meg1334
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a is 19, sin A is 1.16, what do you mean find A?
Hero
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A is an angle. Find it
Hero
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A is an Angle like theta
Hero
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I'm not talking about a = 19. That's a side length
Hero
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\[\sin (A^{\circ}) = 1.169756803\]
I'm talking about Angle A. Find that.
meg1334
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how?
Hero
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You take the inverse sine of both sides to get:
\[\sin^{-1}(A^{\circ}) = \sin^{-1}({1.169756803})
\\A^{\circ} = \sin^{-1}({1.169756803})
\]
Hero
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So compute \[\sin^{-1}({1.169756803})\]
Hero
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Let me know what you get.
meg1334
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it says error
Hero
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Exactly.
Hero
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That's what it should say because no such angle exists.
Hero
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And if the angle doesn't exist, then the triangle can't possibly exist.
Hero
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\[-1< \sin(\theta) < 1\] means that the value of sine can only be between - or + one. So there's no such thing as \(\sin(\theta) = 1.17\)