SOLUTION: Given: A=? a= 6 B= 14.3 b= ? C= ? c=25 Find A A.) {{{ 4.42 }}} B.) {{{ 14.31 }}} C.) {{{ 22.23 }}} D.) {{{ 23.91 }}}

Algebra ->  Test -> SOLUTION: Given: A=? a= 6 B= 14.3 b= ? C= ? c=25 Find A A.) {{{ 4.42 }}} B.) {{{ 14.31 }}} C.) {{{ 22.23 }}} D.) {{{ 23.91 }}}      Log On


   



Question 1068730: Given:
A=? a= 6
B= 14.3 b= ?
C= ? c=25
Find A
A.) +4.42+
B.) +14.31+
C.) +22.23+
D.) +23.91+

Found 2 solutions by Boreal, swincher4391:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
b^2=a^2+c^2-2ac cos B
=36+625=2(6)(25)cos 14.3
=661-290.70
=19.24
sin A/6=sin 14.3/19.24
sin A=6*sin 14.3/19.24
=0.0770
Arc sin 0.0770=4.42 deg
A

Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
Assuming we are talking about triangle ABC we have sides:
a which is opposite angle A
b which is opposite angle B
c which is opposite angle C
We have angle A that is in between sides b and c
We have angle B that is in between sides a and c
We have angle C that is in between sides a and b.
So since we have angle B that is in between sides a and c (and we know all three of these values), this lets us know that we can use the law of cosines.
So
b%5E2+=+a%5E2+%2B+c%5E2+-+2%2Aa%2Ac%2Acos%28B%29
b%5E2+=+6%5E2+%2B+25%5E2+-+2%2A6%2A25%2Acos%2814.3%29
b%5E2+=+370.3
b+=+19.243
We need to find angle A. So since we know side a, side b and angle B, we can use law of sines.
sin%28A%29%2Fa+=+sin%28B%29%2Fb
sin%28A%29+=++a%2Asin%28B%29%2Fb
sin%28A%29+=+6%2Asin%2814.3%29%2F19.243
sin%28A%29+=+0.07701
highlight%28A+=+4.42%29