Question

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

Answer 1

Answer:

Part 1) $z=4\sqrt{3}\ units$

Part 2) $y=4\sqrt{2}\ units$

Part 3) $x=4\sqrt{6}\ units$

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

Find the value of z

In the right triangle DBC

$cos(C)=\frac{4}{z}$ ----> equation A

In the right triangle ABC

$cos(C)=\frac{z}{12}$ ----> equation B

equate equation A and equation B

$\frac{4}{z}=\frac{z}{12}$

$z^{2}=48$

$z=4\sqrt{3}\ units$

step 2

In the right triangle DBC

Applying the Pythagoras Theorem

$z^{2}=y^{2}+4^{2}$

we have

$z=4\sqrt{3}\ units$

substitute

$(4\sqrt{3})^{2}=y^{2}+4^{2}$

$48=y^{2}+16$

$y^{2}=48-16$

$y^{2}=32$

$y=4\sqrt{2}\ units$

step 3

Find the value of x

In the right triangle ABC

Applying the Pythagoras Theorem

$12^{2}=x^{2}+z^{2}$

we have

$z=4\sqrt{3}\ units$

substitute

$12^{2}=x^{2}+(4\sqrt{3})^{2}$

$144=x^{2}+48$

$x^{2}=144-48$

$x^{2}=96$

$x=4\sqrt{6}\ units$