Question

Find the value of x and y. ( ANSWER NEEDS TO BE IN REDUCED RADICAL FORM )

Answer 1

Part 1)
`x=8√(2)\ units`

Part 2)
`y=4√(6)\ units`

Explanation:

see the attached figure with letters to better understand the problem

In the right triangle ABD

Find the length side BD

`sin(45\°)=BD/AB`

`BD=(AB)sin(45\°)`

we have

`AB=8\ units`

`sin(45\°)=(√(2))/(2)`

substitute the given values

`BD=(8)(√(2))/(2)`

`BD=4√(2)\ units`

In the right triangle DBC

Find the length side BC

`sin(30\°)=BD/BC`

`BC=BD/sin(30\°)`

we have

`sin(30\°)=(1)/(2)`

`BD=4√(2)\ units`

substitute the given values

`BC=4√(2)/(1)/(2)`

`BC=8√(2)\ units`

therefore

The value of x is

`x=8√(2)\ units`

In the right triangle DBC

Find the length side DC

`cos(30\°)=DC/BC`

`DC=(BC)cos(30\°)`

we have

`BC=8√(2)\ units`

`cos(30\°)=(√(3))/(2)`

substitute the given values

`DC=(8√(2))(√(3))/(2)`

`DC=4√(6)\ units`

therefore

the value of y is

`y=4√(6)\ units`