Respuesta :

culveryolanda46

Step-by-step explanation:

Using the triangle, we know that

[tex] {27}^{2} + {y}^{2} = {x}^{2} [/tex]

Solving for y^2

[tex] {y}^{2} = {x}^{2} - 27 {}^{2} [/tex]

Likewise,

[tex] {3}^{2} + {y}^{2} = {z}^{2} [/tex]

And finally,

[tex] {x}^{2} + {z}^{2} = 30 {}^{2} [/tex]

Subsituting z^2

[tex] {x}^{2} + 3 {}^{2} + {y}^{2} = 30 {}^{2} [/tex]

Subsitue y^2

[tex] {x}^{2} + 9 + ( {x}^{2} - 27 {}^{2} ) = 900[/tex]

[tex]2 {x}^{2} - 2 {7}^{2} = 891[/tex]

[tex]2 {x}^{2} = 891 + 729[/tex]

[tex]2 {x}^{2} = 1620[/tex]

[tex] {x}^{2} = 810[/tex]

[tex]x = 9 \sqrt{10} [/tex]

[tex]x = 28.5[/tex]

Despina

Answer:

x = 28.46

Step-by-step explanation:

The altitude of a right-angled triangle divides the existing triangle into two similar triangle. Here, the altitude is y.

According to the right triangle altitude theorem, the length of the altitude drawn from the right angle to the hypotenuse is equal to the geometric mean of line segments formed by altitude on the hypotenuse.

The lengths of the segments are 27 and 3.

Solving for x:

[tex] x^2 = (27 + 3) 27 \\ \\ x^2 = 27 \times 30 \\ \\ x^2 = 810 \\ \\ x = \sqrt {810} \\ \\ x = 28.46 \\ \\ [/tex]

Solving for y:

[tex] y^2 = 3 \times 27 \\ \\ y^2 = 81 \\ \\ y = \sqrt{ 81} \\ \\ y = 9 \\ \\ [/tex]

Solving for z :

[tex] z^2 = (27 + 3)3 \\ \\ z^2 = 30 \times 3 \\ \\ z^2 = 90 \\ \\ z = \sqrt{90} \\ \\ z = 9.48 \\ \\ [/tex]

Hence,

  • x = 28.46
  • y = 9
  • z = 9.48
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