Answer:
Difference in the length of AB and AD will be 1.17 units
Step-by-step explanation:
From the figure attached,
In ΔABC and ΔADC,
x = 45°
y = 63°
AC = 4 units
By applying Sine rule in ΔABC,
SinB = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
Sin(x) = [tex]\frac{AC}{AB}[/tex]
Sin(45)° = [tex]\frac{4}{AB}[/tex]
[tex]\frac{1}{\sqrt{2}}=\frac{4}{AB}[/tex]
AB = 4√2 ≈ 5.657 units
Similarly, by applying sine rule in ΔADC,
Sin(y)° = [tex]\frac{AC}{AD}[/tex]
Sin(63)° = [tex]\frac{4}{AD}[/tex]
AD = [tex]\frac{4}{\text{Sin}63}[/tex]
= 4.489 units
AB - AD = 5.657 - 4.489
= 1.168
≈ 1.17 units
Therefore, difference in the length of AB and AD will be 1.17 units
