Question

Which of the following represent the values of x, y, and z.

Answer 1

B

Explanation:

Test Yourself

Answer 2

Part 1)
`z=4√(3)\ units`

Part 2)
`y=4√(2)\ units`

Part 3)
`x=4√(6)\ units`

Explanation:

see the attached figure with letters to better understand the problem

step 1

Find the value of z

In the right triangle DBC

`cos(C)=(4)/(z)` ----> equation A

In the right triangle ABC

`cos(C)=(z)/(12)` ----> equation B

equate equation A and equation B

`(4)/(z)=(z)/(12)`

`z^(2)=48`

`z=4√(3)\ units`

step 2

In the right triangle DBC

Applying the Pythagoras Theorem

`z^(2)=y^(2)+4^(2)`

we have

`z=4√(3)\ units`

substitute

`(4√(3))^(2)=y^(2)+4^(2)`

`48=y^(2)+16`

`y^(2)=48-16`

`y^(2)=32`

`y=4√(2)\ units`

step 3

Find the value of x

In the right triangle ABC

Applying the Pythagoras Theorem

`12^(2)=x^(2)+z^(2)`

we have

`z=4√(3)\ units`

substitute

`12^(2)=x^(2)+(4√(3))^(2)`

`144=x^(2)+48`

`x^(2)=144-48`

`x^(2)=96`

`x=4√(6)\ units`