Law of sine SSA

Question

Side a= 6

side b=8

angle A =35

determine if it’s 1,2 or no triangles and solve all triangles

please give full answer

Ex side b=1

Answer 1

always use law of cosine for SSA problems first to determine whether there is 0,1, or 2 triangles valid.

here 6²=c²+8²-2c*8*cos(35) si quadradic in c

corrections involve more careful attention to decimals in calculator

two triangles, c1=2.69

c2=10.41

now use law of sin to compute angle C (angle B=180-A-C)

the following is the result.

traingle1, a=6, b=8, c=2.69 Angle A=35 degrees, B=130.1 degrees, C=14.9 degrees

triangle 2, a=6, b=8, c=10.41 Angle A= 35 degrees, B=60 degrees, C= 85 degrees

check work, (sin(35))/6=.096,,,(sin(130.1))/8=.096,,,(sin(14.9))/2.69=.096

check work, (sin(35))/6=.096,,,(sin(60))/8 not close to .096 so there is something wrong with triangle 2

the problem is while angle C was computed to be 85 degrees, from law of sin, it is by nature of sin that sin (180-85)=sin(95)=sin(85)

let's try triangle 2, a=6, b=8, c=10.41 Angle A=35 degrees, B=50 degrees, C=95 degrees

check work, (sin(35))/6=.096,,,(sin(50))/8=.096,,,(sin(95))/10.41=.096

final answer

traingle1, a=6, b=8, c=2.69 Angle A=35 degrees, B=130.1 degrees, C=14.9 degrees

triangle 2, a=6, b=8, c=10.41 Angle A= 35 degrees, B=50 degrees, C= 95 degrees

Answer 2

2 obtuse triangles

1st is 35 -49.89 - 95.15 angles with opposite sides 6 -8- 12.19

obtuse is 14.89 - 35 - 130.11 angles with opposite sides 2.69 - 6 - 8

use Law of Sines

sin35/6 = .0956 = sinB/8

sinB = 8(.0956) = .7648

B =49.89 or 130.11

C =95.15 or 14.89

c= 12.19 or 2.69