The sides and angles of a triangle can be determined using trigonometry ratios
The values of x, y and z are [tex]x = 14\sqrt 2[/tex], [tex]y =14[/tex] and [tex]z = 14\sqrt 3[/tex]
How to determine the missing values of the triangle
The upper triangle is a right triangle with an angle measure of 45 degrees.
So, the value of x is:
[tex]x = 14\sqrt 2[/tex]
Next, we calculate the hypotenuse (h) of the lower triangle using:
[tex]h^2 = (14\sqrt 2)^2 + (14\sqrt 2)^2[/tex]
So, we have:
[tex]h^2 = 784[/tex]
Take the square roots of both sides
[tex]h = 28[/tex]
The value of y is then calculated using the following sine ratio
[tex]\sin(30) = \frac y{28}[/tex]
Make y the subject
[tex]y =28 * \sin(30)[/tex]
Evaluate
[tex]y =14[/tex]
The value of z is then calculated using the following cosine ratio
[tex]\cos(30) = \frac z{28}[/tex]
Make z the subject
[tex]z =28 * \cos(30)[/tex]
Evaluate
[tex]z =28 * \frac{\sqrt 3}{2}[/tex]
[tex]z = 14\sqrt 3[/tex]
Hence, the values of x, y and z are [tex]x = 14\sqrt 2[/tex], [tex]y =14[/tex] and [tex]z = 14\sqrt 3[/tex]
Read more about right triangles at:
https://brainly.com/question/14628284
