Use the Law of Sines to solve the triangle. Round your answers to two decimal places. A = 81° 40', C = 54.5°, c = 15.3

Answer 1

Use the Law of Sines to solve the triangle. Round your answers to two decimal places. A = 81° 40', C = 54.5°, c = 15.3

Detailed Solution:

Simply: In this problem, here is what is given and missing:

Angles: A = 81° 40' B = ?? C = 54.5° = 54° 30' Sides: a = ?? b = ?? c = 15.3

Find Angle: B = 180° – (A + C)=> B = 180° – (81° 40' + 54° 30')=> B = 180° – 136° 10'=> B = 43° 50'

Use Law of Sines to find side a and side b: a/sin A = b/sin B = c/sin C

Find side a: a/sin A = c/sin C=>a = (c)(sin A)/(sin C)=>a = (15.3)(sin 81° 40') / (sin 54° 30')=>a = 18.59

Find side b: b/sin B = c/sin C=>b = (c)(sin B)/(sin C)=>b = (15.3)(sin 43° 50') / (sin 54° 30')=>b = 13.02

Therefore, here is the complete solution:

Angles: A = 81° 40' B = 43° 50' C = 54° 30' Sides: a = 18.59 b = 13.02 c = 15.3