Respuesta :

fieryanswererft

Answer:

  • x = 466.7 ft
  • y = 240.3 ft

First find the inner angle:

  • 90° - 31°
  • 59°

using sine rule:

[tex]\sf sin(x)= \dfrac{opposite}{hypotensue}[/tex]

[tex]\hookrightarrow \sf sin(59)= \dfrac{400}{x}[/tex]

[tex]\hookrightarrow \sf x = \dfrac{400}{sin(59)}[/tex]

[tex]\hookrightarrow \sf x = 466.6533[/tex]

[tex]\hookrightarrow \sf x = 466.7[/tex]   ( rounded to nearest tenth )

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using tan rule:

[tex]\sf tan(x)= \dfrac{opposite}{adjacent}[/tex]

[tex]\hookrightarrow \sf tan(59)= \dfrac{400}{y}[/tex]

[tex]\hookrightarrow \sf y= \dfrac{400}{ tan(59)}[/tex]

[tex]\hookrightarrow \sf y= 240.344[/tex]

[tex]\hookrightarrow \sf y= 240.3[/tex]

semsee45

Answer:

y = 466.7 ft (nearest tenth)

Step-by-step explanation:

Using the Alternate Interior Angle Theorem
the angle inside the triangle that is opposite the side [tex]y[/tex] is 31°

Using the cos trig ratio:

[tex]\sf cos(\theta)=\dfrac{A}{H}[/tex]

where:

  • [tex]\theta[/tex] is the angle
  • A is the side adjacent the angle
  • H is the hypotenuse

Given:

  • [tex]\theta[/tex] = 31°
  • A = 400 ft
  • H = [tex]x[/tex]

Substitute given values and solve for x:

[tex]\sf \implies cos(31)=\dfrac{400}{x}[/tex]

[tex]\sf \implies x=\dfrac{400}{cos(31)}[/tex]

[tex]\sf \implies x=466.7\:ft\:(nearest\:tenth)[/tex]

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