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.
