Respuesta :

fieryanswererft

Answer:

  • y = 242.4
  • x = 437.3

First find the inner angle:

  • 90° - 29°
  • 61°

[ given hypotenuse = 500 ft ]

using sine rule:

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

[tex]\hookrightarrow \sf sin(61)= \dfrac{x}{500}[/tex]

[tex]\hookrightarrow \sf x=sin(61)*500[/tex]

[tex]\hookrightarrow \sf x=437.3[/tex]

using pythagoras theorem:

  • a² + b² = c²
  • y² + (437.3)² = 500²
  • y = √58760.1
  • y = 242.4
semsee45

Answer:

y = 242.4 ft (nearest tenth)

Step-by-step explanation:

Using the Alternate Interior Angle Theorem
the angle opposite side [tex]y[/tex] is 29°

Using the sine trig ratio:

[tex]\sf sin(\theta)=\dfrac{O}{H}[/tex]

where:

  • [tex]\theta[/tex] is the angle
  • O is the side opposite the angle
  • H is the hypotenuse

Given:

  • [tex]\theta[/tex] = 29°
  • O = [tex]y[/tex]
  • H = 500 ft

Substitute given values and solve for y:

[tex]\sf \implies sin(29)=\dfrac{y}{500}[/tex]

[tex]\sf \implies y=500sin(29)[/tex]

[tex]\sf \implies y=242.2\:ft\:(nearest\:tenth)[/tex]

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