Question

Please Help! Geometry!

Answer 1

Answer:  The perimeter of angle ABC = 61.911  Step-by-step explanation:  Since we are given two angles and the length of one side, we apply the SINE RULE  Sine Rule = sinA / a  = sinB / b = sinC / c  where A, B, C are the angles of the triangle AND a, b and c are the length of the sides of the triangle.  BUT FIRST, lets get the value for the missing angle CAB  Sum of angles of a triangle = 180° angle CAB = 180° - (40° +  49° ) angle CAB = 180° - 89 CAB = 91°  To get the PERIMETER of  ΔABC, we must get the length of all the three sides of the triangle using THE SINE RULE  sin49° / 19.5  =  sin 40° / AB  =  sin91° / CB  0.755/19.5  = 0.643 / AB Cross multiplying AB * 0.755  =  0.643 * 19.5 AB = 12.539 / 0.755 AB = 16.608   LETS SOLVE FOR CB sin49° / 19.5 = sin91° / CB CB * sin49° = 19.5 * sin91° CB * 0.755 = 19.5 * 0.999 CB = 19.481 / 0.755 CB = 25.803  Therefore,  AC = 19.5 AB = 16.608 CB = 25.803  The perimeter of ΔABC equals to the sum of AC, AB, CB = 19.5 + 16.608 + 25.803 = 61.911.