Question

Find the value of x and the value of y.

A. x= 2 root 2, y = 8
B. X= 2, y = 4 root 6
C. X = 2 root 2, y=2 root 6
D. X = 2 root 3, y=6 root 3

Answer 1

Option C.

`x=2√(2)`

`y=2√(6)`

Explanation:

step 1

Find the value of x

In the right triangle of the figure

`sin(30\°)=(x)/(4√(2))` -----> opposite side angle of 30 degrees divided by the hypotenuse

Remember that

`sin(30\°)=(1)/(2)`

so

`(1)/(2)=(x)/(4√(2))`

`x=(4√(2))/(2)`

`x=2√(2)`

step 2

Find the value of y

In the right triangle of the figure

`cos(30\°)=(y)/(4√(2))` -----> adjacent side angle of 30 degrees divided by the hypotenuse

Remember that

`cos(30\°)=(√(3))/(2)`

so

`(√(3))/(2)=(y)/(4√(2))`

`y=(4√(6))/(2)`

`y=2√(6)`