Question

HELPPPPPP (25 POINTSSS) WILL GIVE YOU THE BRAINLIEST!!!!!!

Answer 1

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