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
