(25 pointsss) will give you the solve this triangle: a = 26, b = 29, a = 58 degreesif it has 0 solutions, say so. if it has 1 solution, state the solution. if it has 2 solutions, state both solutions. round all angles and sides to the nearest tenth. for this problem, you do not need to show your work. just give the answers.

we know that

step 1

applying the law of sines

find the angle B

a/sin A=b/sin B> solve for sin B

sin B=(b/a)*sin A> sin B=(29/26)*sin 58> sin B=0.9459

B=arc sin(0.9459)> B=71.07> B=71.1°

step 2

Find the angle C

we know that

A+B+C=180°> C=180-(58+71.1)> C=50.9°

Step 3

Find the measure of side c

applying the law of sines

a/sin A=c/sin C> solve for c

c=a*(sin C/sin A)> c=26*(sin 50.9/sin 58)> c=23.79> c=23.8

the first solution is

A=58° B=71.1° C=50.9°

a=26 b=29 c=23.8

step 4

second solution

Find the new angle B

B=180°-71.1°> B=108.9°

Step 5

Find the new angle C

we know that

A+B+C=180°> C=180-(58+108.9)> C=13.1°

Step 6

Find the new measure of side c

applying the law of sines

a/sin A=c/sin C> solve for c

c=a*(sin C/sin A)> c=26*(sin 13.1/sin 58)> c=6.95> c=7

the second solution is

A=58° B=108.9° C=13.1°

a=26 b=29 c=7

the answer is

the problem has 2 solutions