SOLUTION: Find the measure of angle x, if possible. Notice that x is an obtuse angle. Round to the nearest tenth. (If not possible, enter IMPOSSIBLE.) https://www.webassign.net/waplots/c/5/

Algebra ->  Trigonometry-basics -> SOLUTION: Find the measure of angle x, if possible. Notice that x is an obtuse angle. Round to the nearest tenth. (If not possible, enter IMPOSSIBLE.) https://www.webassign.net/waplots/c/5/      Log On


   

Question 1204461: Find the measure of angle x, if possible. Notice that x is an obtuse angle. Round to the nearest tenth. (If not possible, enter IMPOSSIBLE.)
https://www.webassign.net/waplots/c/5/1cba6911d1f6486f328dd2e913c145.gif
Found 3 solutions by mccravyedwin, MathLover1, ikleyn:
Answer by mccravyedwin(408) About Me  (Show Source):
You can put this solution on YOUR website!


By the law of sines,

30%5E%22%22%2Fsin%28x%5E%22%22%29%22%22=%22%2225%5E%22%22%2Fsin%2854%5Eo%29

Cross-multiply:

25%2Asin%28x%5E%22%22%29%22%22=%22%2230%2Asin%2854%5Eo%29

sin%28x%5E%22%22%29%22%22=%22%2230%2Asin%2854%5Eo%29%2F25

sin%28x%29%5E%22%22%22%22=%22%220.9708203932

Notice that when you use sin-1, your calculator gives 
you 76.12480522o, but remember that the sine is positive
in QI and QII, and you are warned that x is a QII angle 
because it is obtuse, so 76.12480522o is the reference
angle of x, so we subtract: 

180o-76.12480522o = 103.875194876o, which rounds to 103.9o.

Edwin

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
a=25
c=30
angle B=54°
use the law of cosine to calculate side+b
b=+sqrt%28a%5E2%2Bc%5E2-2ac%2Acos%28B%29%29
b=+sqrt%2825%5E2%2B30%5E2-2%2A25%2A30%2Acos%2854%29%29
b=+25.3638

now find angle x (actually angle C)

x=cos%5E-1%28%28a%5E2%2Bb%5E2-c%5E2%29%2F2ab%29
x=cos%5E-1%28%2825%5E2%2B25.3638%5E2-30%5E2%29%2F%282%2A25%2A25.3638%29%29
x=73.1°
third angle is
A=180-%28B%2Bx%29
A=180-%2854%2B73.1%29
A=52.9°

Answer: x=73.1°
complete solution:
Sides:
a+=+25
b+=+25.3638
c+=+30
Angles:
A+=+52.9 °
B+=+54+°
C=x=+73.1 °



Answer by ikleyn(52824) About Me  (Show Source):
You can put this solution on YOUR website!
.

The  " solution "  in the post by  @MathLover1 is  INCORRECT.


It is incorrect from the very beginning,  since madam incorrectly uses the cosine law.


For safety of your mind,  simply ignore her post,
as if you  NEVER  have seen it before.