Answer: Line AB = 5.2
Step-by-step explanation: We start with triangle ACD, with two sides given and angle A which shall be the reference angle can be calculated as,
SinA = opposite/hypotenuse
Where the opposite is 4.3 (line facing the reference angle) and the hypotenuse is 5.6 (line facing the right angle)
SinA = 4.3/5.6
SinA = 0.7679
By use of a calculator or a table of values
A = 50.17 degrees.
Having been told that both angles DAC and BAD are equal, then we move to triangle ADB where the reference angle is 50.17 (BAD) and the opposite is 4 (line facing the reference angle) and the unknown side is the hypotenuse (line AB).
Sin 50.17 = opposite/hypotenuse
Sin 50.17 = 4/AB
0.7679 = 4/AB
By cross multiplication we now have
AB = 4/0.7679
AB = 5.2090
Approximately to one decimal place,
AB = 5.2 units
