My teacher hasn't done any examples with us on how to solve SSA questions when the given angle is obtuse, and I don't know what to do even though I'm sure the answer is obvious!
The given values are:
Angle A= 112 degrees
side a = 9
side b = 4
What do I do?
(I asked this question yesterday but I didn't get the answer I was looking for.....)
Thank you!
The given values are:
Angle A= 112 degrees
side a = 9
side b = 4
What do I do?
(I asked this question yesterday but I didn't get the answer I was looking for.....)
Thank you!
-
why should it be any different than with a given acute angle? it will be easier in one sense, though...
sin A / a = sin B / b
sin 112 / 9 = sin B / 4
4 sin 112 / 9 = sin B
.4121 = sin B
B = sin^-1 .4121 = 24.3 degrees
(B = 180 - 24.3 = 155.7 clearly will not work in a triangle where A = 112 already)
A = 112 ; B = 24.3 , C = 43.7 (angles sum to 180)
you can then find c using the law of sines again:
sin 112 / 9 = sin 43.7 / c ==> c = 9 sin 43.7 / sin 112
given an obtuse angle in the SSA case means there will only be one solution (if a solution exists)
sin A / a = sin B / b
sin 112 / 9 = sin B / 4
4 sin 112 / 9 = sin B
.4121 = sin B
B = sin^-1 .4121 = 24.3 degrees
(B = 180 - 24.3 = 155.7 clearly will not work in a triangle where A = 112 already)
A = 112 ; B = 24.3 , C = 43.7 (angles sum to 180)
you can then find c using the law of sines again:
sin 112 / 9 = sin 43.7 / c ==> c = 9 sin 43.7 / sin 112
given an obtuse angle in the SSA case means there will only be one solution (if a solution exists)
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You break it into smaller triangles which will have a 90 deg. angle.