Use the law of sines to solve the triangle. Round answers to two decimal places

Question

B= 30 degrees 

C= 107 degrees 

a= 3 5/8 

Answer 1

Greetings! Lets solve this shall we ?

So, we must use the Law of Sines to solve this triangle given Angle B = 30 degrees and Angle C = 107 degrees and side a = 3.625 after translating the mixed number into a decimal. We can immediately find angle A such that 180 - (107+30) = 180 - 137 = 43 degrees. Now, we can use the Law of Sines to solve for the other two sides b and c such that

sinA / a = sinB / b

sin43 / 3.625 = sin30 / b...........We cross multiply such that

bsin43 = 3.625sin30......Then divide sin43 to obtain

b = 2.658 after putting (3.625sin30/sin43) in the calculator. Finally, we can find side c with

sin30 / 2.658 = sin107 / c.........We then cross multiply to get

csin30 = 2.658sin107.........Then divide sin30 to obtain

c = 5.083 after putting (2.658sin107/sin30) in the calculator!

I hope this helped!