SOLUTION: In triangle ABC angle m < A is 45 degrees, angle m < B=30 degrees, and side a=10. What is the side b of the trangle?

Question 1197857: In triangle ABC angle m < A is 45 degrees, angle m < B=30 degrees, and side a=10. What is the side b of the trangle?
Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39623) (Show Source): You can put this solution on YOUR website!
That does not display. Do it like THIS:

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In triangle ABC angle m < A is 45 degrees, angle m < B=30 degrees, and side a=10. What is the side b of the trangle?
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Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

I have edited your question to add in the necessary spaces, so that the full question is visible.
The issue is that the less than sign needs space on both sides.

Question:
In triangle ABC angle m < A is 45 degrees, angle m < B=30 degrees, and side a=10. What is the side b of the triangle?

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Solution:

It helps to draw out what we know so far.

Convention is to have the uppercase letters represent angles, while the lowercase letters are side lengths.
Angle A is opposite side 'a'
Angle B is opposite side 'b'
Angle C is opposite side 'c'

Use the law of sines to determine side b
sin(A)/a = sin(B)/b
b*sin(A) = a*sin(B) .... cross multiply
b = a*sin(B)/sin(A) .... divide both sides by sin(A)
b = 10*sin(30)/sin(45)
b = 7.07106781186548 approximately
Round that however your teacher instructs.
Make sure your calculator is in degree mode.

Extra info:
If you want to find side c, then you'll need to find angle C first.
Use the fact that the interior angles of a triangle add to 180, so A+B+C = 180

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