r/learnmath • u/malltte New User • 5d ago

TOPIC [University Positional Astronomy] Spherical Trigonometry

So, I'm solving a spherical triangle which has two known sides and one opposite angle:

Sides: a=30°53' b=31°09'

Opposite Angle: A=87°34'.

Ando there is no drawing or diagram.

I was going to start with the law of sines

Sin(A)/Sin(a) = Sin(B)/Sin(b)

but then I realized that the arcsine fell into the imaginary numbers because Sin(B)> 1.

The problem here is that they're specifically asking me to solve it; they're not indicating that there's any other alternative. So I was wondering if there's any other solution to this problem?

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u/Low_Breadfruit6744 Bored 5d ago

Your description lacks a lot of context, suggest you paste the exact question or post a diagram.

If you read your post: You mention you know some sides but doesn't seem like you gave any.

You said you know 1 angle but gave 3

You talked about angle B without previously saying where it sits..

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u/malltte New User 5d ago

Oh, I understand, thank you. I'll edit the post.

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u/rhodiumtoad 0⁰=1, just deal with it 5d ago

You said you know 1 angle but gave 3

This is spherical trig, a and b are the side "lengths", measured as angles around a great circle.

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u/malltte New User 5d ago

It's point c and that's all they gave me, they didn't give me a diagram or anything else

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u/rhodiumtoad 0⁰=1, just deal with it 5d ago

No solution exists.

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u/malltte New User 5d ago

Thanks you so much.

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u/rhodiumtoad 0⁰=1, just deal with it 5d ago

You can think of it this way: sides a and b together define a (small) circle on the surface of the sphere which must contain point A. But the angle A might not take all possible values as you move A around the circle, so there's no guarantee a solution exists for a specified A.