Question

Find x, y and z.

( ANSWER NEEDS TO BE IN REDUCED RADICAL FORM )

Answer 1

Answer:

Part 1) $x=6\sqrt{2}\ units$

Part 2) $y=4\sqrt{3}\ units$

Part 3) $z=8\sqrt{3}\ units$

Step-by-step explanation:

In the right triangle of the right side

$cos(45\°)=\frac{\sqrt{2}}{2}$

$cos(45\°)=\frac{x}{12}$

$\frac{x}{12}=\frac{\sqrt{2}}{2}$

$x=6\sqrt{2}\ units$

In the right triangle of the left side

$tan(60\°)=\frac{12}{y}$

$tan(60\°)=\sqrt{3}$

$\sqrt{3}=\frac{12}{y}$

$y=\frac{12}{\sqrt{3}}$

Simplify

$y=12\frac{\sqrt{3}}{3}$

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

In the right triangle of the left side

$sin(60\°)=\frac{12}{z}$

$sin(60\°)=\sqrt{3}/2$

$\sqrt{3}/2=\frac{12}{z}$

$z=\frac{24}{\sqrt{3}}$

Simplify

$z=24\frac{\sqrt{3}}{3}$

$z=8\sqrt{3}\ units$

Answer 2

Answer:

$x =6\sqrt{2}$

$y=4\sqrt{3}$

$z =8\sqrt{3}$

Step-by-step explanation:

The cosine function is defined as:

$cos(b) = \frac{adjacent}{hypotenuse}$

Where:

adjacent is the length of the side that contains angle b and angle 90 °

Hypotenuse is the length of the side opposite the angle of 90 °.

So if b is the angle of 45 ° we have that:

$adjacent = x\\hypotenuse = 12$

Thus:

$cos(45\°) = \frac{x}{12}$

Now we solve the equation for x

$x = cos(45\°)*12$

$x =6\sqrt{2}$

The sine function is defined as:

$cos(b) = \frac{opposite}{hypotenuse}$

Where:

opposite is the length of the side opposite the angle of b

Hypotenuse is the length of the side opposite the angle of 90 °.

if b is the angle of 60 ° we have that:

$opposite = 12\\hypotenuse = z$

Thus:

$sin(60\°) = \frac{12}{z}$

Now we solve the equation for z

$z = \frac{12}{sin(60\°)}$

$z =8\sqrt{3}$

Finally we use the cosine function to find the value of y

if b is the angle of 60 ° we have that:

$adjacent = y\\hypotenuse = 8\sqrt{3}$

Thus:

$cos(60\°) = \frac{y}{8\sqrt{3}}$

Now we solve the equation for y

$y = 8\sqrt{3}*cos(60\°)$

$y=4\sqrt{3}$