Solve the triangle ABC, if the triangle exists. B = 39 degree 54\' a = 37.2 b =
ID: 3015652 • Letter: S
Question
Solve the triangle ABC, if the triangle exists. B = 39 degree 54' a = 37.2 b = 31.2 Select the correct choice below and fill in the answer boxes within the choice. There are 2 possible solutions for the triangle. The measurements for the solution with the longer side c are as follows. m angle A = ___ degree ___' m angle C = ____ degree ____' (Simplify your answer Round to the nearest degree as needed. Round to the nearest minute needed.) The length of side c = ____ (Round to the nearest tenth as needed.) The measurements for the solution with the shorter side c are as follows. m angle A = ___ degree ___' m angle C = ____ degree ____' (Simplify your answer Round to the nearest degree as needed. Round to the nearest minute needed.) The length of side c = ____ (Round to the nearest tenth as needed.) There is only 1 possible solution for the triangle. The measurements for the remaining angles A and C and side c are as follows. m angle A = ___ degree ___' m angle C = ____ degree ____' (Simplify your answer Round to the nearest degree as needed. Round to the nearest minute needed.) The length of side c = ____ (Round to the nearest tenth as needed.) There are no possible solutions for this triangle.Explanation / Answer
B = 39deg 54 min = 39.9 deg; a = 37.2 ; b = 31.2
use sine law: a/sinA = b/sinB
sinA = a*sinB/b = 37.2*sin39.9/31.2 = 0.7648
A1 = 49.88 deg; A2 = 180 - 49.88 = 130.11 deg
C1 = 180 -B - A1 = 90.22 ; C2 = 180 - A2 - B = 9.9 deg
there are two traingles possible
c/sinC1 = a/sinA1
c1 =sin90.22*27.2/sin49.88 = 35.57
c2 = sin9.9*27.2/sin130.11 = 6.11
c with longer side : A = 49.88 deg =49 deg 53 min ; C = 90 deg13 min ; c = 35.6
c with shorter side : A= 130 deg 7 min ; C = 9 deg 54 min; c= 6.1