Question

What is the length of the side labeled x?

Answer 1

AB = 42.15 units

Explanation:

In triangle ABD,

By applying Cosine rule in this triangle,

cos(30)°=
`\frac{\text{Adjacent side}}{\text{Hypotenuse}}`

`(√(3) )/(2)` =
`(AD)/(AB)`

`(√(3))/(2)=(AD)/(47)`

AD =
`(47√(3))/(2)`

By applying tangent rule in ΔACD,

tan(44)° =
`\frac{\text{Opposite side}}{\text{Adjacent side}}`

tan(44)° =
`(AD)/(x)`

0.9657 =
`((47√(3))/(2))/(x)`

0.9657 =
`(47√(3))/(2x)`

x =
`(47√(3))/(2(0.9657))`

x = 42.15

≈ 42.2 units