Question

Help, please:
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

Answer 1

http://www.regentsprep.org/Regents/math/algtrig/ATT12/lawofsinesAmbiguous.htm

Answer 2

No triangle is formed, (the system cannot be solved )

Answer 3

set up a ratio, using the law of sines
\[ \frac{c}{\sin C} = \frac{a}{\sin A} \]
in this case, replace c with 10, C with 38º and a with 19
\[ \frac{10}{\sin 38º} = \frac{19}{\sin A} \]
I would flip the fractions to get
\[ \frac{\sin 38º} {10}= \frac{\sin A}{19} \]
then multiply both sides by 19
\[ \frac{19\cdot \sin 38º} {10}= \frac{\cancel{19}\cdot\sin A}{\cancel{19}} \]
to get
\[ \sin A = 1.9 \sin(38º) \]
now get a calculator and figure out 1.9*sin(38)
you get 1.17
if you try to find the inverse sin of 1.17 you get a math error (sin only goes up to 1)
so there is no solution

Answer 4

@phi thank you so much. Do you mind helping me with one or two more? :o)

Answer 5

post the problem