SOLUTION: Use the Law of Sines to solve, if possible, the missing side or angle for the triangle or triangles in the ambiguous case. Round your answer to the nearest tenth. (If not possible,

Algebra ->  Trigonometry-basics -> SOLUTION: Use the Law of Sines to solve, if possible, the missing side or angle for the triangle or triangles in the ambiguous case. Round your answer to the nearest tenth. (If not possible,      Log On


   

Question 1204424: Use the Law of Sines to solve, if possible, the missing side or angle for the triangle or triangles in the ambiguous case. Round your answer to the nearest tenth. (If not possible, enter IMPOSSIBLE.)
Find angle A when
a = 23,
b = 9,
B = 28°.
Found 2 solutions by MathLover1, math_tutor2020:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Find angle A when
a+=+23
b+=+9
B+=+28°
use the Law of Sines:
a%2Fsin%28A%29=b%2Fsin%28B%29
23%2Fsin%28A%29=9%2Fsin%2828%29
23sin%2828%29=9sin%28A%29
sin%28A%29=%2823sin%2828%29%29%2F9
sin%28A%29=1.199760660452832
A=sin%5E-1%281.199760660452832%29
A=1.570796326794897+-0.6220015679413891%2Ai
there is no real solution
For ASS (SSA) theorem sin%28B%29+%3E+b%2Fa so there are+no solutions and no+triangle!

answer: IMPOSSIBLE


Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Law of Sines
sin(A)/a = sin(B)/b
sin(A) = a*sin(B)/b
sin(A) = 23*sin(28)/9
sin(A) = 1.19976 approximately

At this point we can stop.
There aren't any real number solutions because the range of y = sin(x) is -1+%3C=+y+%3C=+1
The largest sin(A) can get is sin(A) = 1.

Therefore, a triangle is not possible.