Solve the triangle ABC if the triangle exists A 445 degree

Solve the triangle ABC, if the triangle exists. A = 44.5 degree, a = 8.5 m b = 10.9 m Select the correct choice below and fill in the answer boxes within the choice. A. There are 2 possible solution for the triangle. The measurements for the solution with the longer side c are as follows. m angle B = degree m angle C = degree The length of side c = The measurements for the solution with the shorter side c are as follows m angle A = degree m angle C = degree The length of side c = B. There are 1 possible solutions for the triangle. The measurements for the remaining angles B and C and side c are as follows. m angle B = degree m angle C = degree The length of side c = C. There are no possible solutions for the triangle.

Solution

We have given A=44.5⁰ a=8.5 m,b=10.9 m

by using Law of sines a/sinA =b/sinB =c/sinC

substitute we known values

8.5/sin44.5⁰=10.9/sinB

then sinB=(10.9*sin44.5⁰)/8.5 since by cross multiplication

sinB=0.89881305657,B=arcsin(0.89881305657)=64⁰

now we know the A=44.5⁰ , B=64⁰

C=180-(A+B)=180-(44.5+64)=71.5⁰

a/sinA =c/sinC

8.5/sin(44.5)=c/sin(71.5)

c=(8.5/sin(44.5))*sin(71.5)=11.5 m

m<B=64⁰,m<C=71.5⁰ and c=11.5m

answer is option B