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Find x. Leave answers in simplified radical form. (Step by step)

Find X Leave Answers In Simplified Radical Form Step By Step class=

Sagot :

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Answer:

[tex]\sf x = 4\sqrt{2}[/tex]

Given:

  • adjacent: 4 cm
  • hypotenuse: x cm
  • angle: 45°

using cosine rule:

[tex]\sf cos(x) = \dfrac{adjacent}{hypotenuse}[/tex]

[tex]\sf cos(45) = \dfrac{4}{x}[/tex]

[tex]\sf x = \dfrac{4}{cos(45)}[/tex]

[tex]\sf x = 4\sqrt{2}[/tex]

Solution:

Step-1: Find the missing angle.

  • 90 + 45 + y = 180
  • => 135 + y = 180
  • => y = 180 - 135
  • => y = 45°

Step-2: Review the following.

  • This triangle is an isosceles right triangle because two angles are equivalent.
  • Two sides of the triangle must equal 4 cm.

Step-3: Use Pythagoras theorem.

  • x² = 4² + 4²
  • => x² = 16 + 16
  • => x = √32 ≈ 5.65 cm (Using calculator)
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