Question

If x = 45, y = 63, and the measure of AC = 4 units, what is the difference in length between segments AB and AD? Round your answer to the nearest hundredth.

Answer 1

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 = $\frac{\text{Opposite side}}{\text{Hypotenuse}}$

Sin(x) = $\frac{AC}{AB}$

Sin(45)° = $\frac{4}{AB}$

$\frac{1}{\sqrt{2}}=\frac{4}{AB}$

AB = 4√2 ≈ 5.657 units

Similarly, by applying sine rule in ΔADC,

Sin(y)° = $\frac{AC}{AD}$

Sin(63)° = $\frac{4}{AD}$

AD = $\frac{4}{\text{Sin}63}$

     = 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