Respuesta :

calculista

Answer:

Part 1) [tex]x=14\sqrt{2}\ units[/tex]

Part 2) [tex]y=14\ units[/tex]

Part 3) [tex]z=14\sqrt{3}\ units[/tex]

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

In the right triangle ABC

we know that

The triangle ABC is a [tex]45^o-90^o-45^o[/tex]

so

Is an isosceles right triangle

The legs are equal

therefore

AC=AB

[tex]x=14\sqrt{2}\ units[/tex]

step 2

Find the length side BC

Applying the Pythagorean Theorem]

[tex]BC^2=AB^2+AC^2[/tex]

[tex]BC^2=(14\sqrt{2})^2+(14\sqrt{2})^2[/tex]

[tex]BC^2=784\\BC=28\ units[/tex]

step 3

Find the value of y

In the right triangle BCD

[tex]sin(30^o)=\frac{BD}{BC}[/tex] ----> by SOH (opposite side divided by the hypotenuse)

[tex]sin(30^o)=\frac{y}{28}[/tex]

Remember that

[tex]sin(30^o)=\frac{1}{2}[/tex]

so

[tex]\frac{y}{28}=\frac{1}{2}\\\\y=14\ units[/tex]

step 4

Find the value of z

In the right triangle BCD

[tex]cos(30^o)=\frac{DC}{BC}[/tex] ----> by CAH (adjacent side divided by the hypotenuse)

[tex]cos(30^o)=\frac{z}{28}[/tex]

Remember that

[tex]cos(30^o)=\frac{\sqrt{3}}{2}[/tex]

so

[tex]\frac{z}{28}=\frac{\sqrt{3}}{2}\\z=14\sqrt{3}\ units[/tex]

Ver imagen calculista
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The value of x, y, and z is [tex]14\sqrt2,14,\rm\; and \;14\sqrt3[/tex], respectively.

Given information:

From the given figure, the following information can be extracted:

  • The upper right triangle has angles 45, 45, and 90 degrees.
  • One leg of the upper triangle is [tex]14\sqrt2[/tex]. So, the other leg will also be [tex]14\sqrt2[/tex].
  • The lower right triangle has angles 30, 60, and 90 degrees.

Use Pythagoras theorem for upper triangle to get the value of hypotenuse as,

[tex]h^2=(14\sqrt2)^2+(14\sqrt2)\\h=28[/tex]

So, the value of x is [tex]14\sqrt2[/tex] and the hypotenuse is 28 units.

Now, for lower triangle,

[tex]sin30=\dfrac{y}{28}\\\dfrac{1}{2}=\dfrac{y}{28}\\y=14\\cos30=\dfrac{z}{28}\\\dfrac{\sqrt3}{2}=\dfrac{z}{28}\\z=14\sqrt3[/tex]

Therefore, the value of x, y, and z is [tex]14\sqrt2,14,\rm\; and \;14\sqrt3[/tex], respectively.

For more details, refer to the link:

https://brainly.com/question/15894165

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