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

Difference in the length of AB and AD will be 1.17 units

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) =
`(AC)/(AB)`

Sin(45)° =
`(4)/(AB)`

`(1)/(√(2))=(4)/(AB)`

AB = 4√2 ≈ 5.657 units

Similarly, by applying sine rule in ΔADC,

Sin(y)° =
`(AC)/(AD)`

Sin(63)° =
`(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