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Consider the right triangle with hypotenuse 5, horizontal leg x , vertical leg y , and angle ∅ opposite y. How can we view x as depending on y? How can we view x as depending on ∅ ? Explain by using appropriate relationships in the triangle and writing x both as a function of y and as a function of ∅ .

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Answer:

  • x = √(25 -y²)
  • x = 5cos(Ф)

Step-by-step explanation:

The Pythagorean theorem relates the sides of a right triangle.

  x² + y² = 5²

  x² = 25 -y²

  x = √(25 -y²)

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The cosine function relates the adjacent side and the hypotenuse of an acute angle in a right triangle.

  Cos = Adjacent/Hypotenuse

  Adjacent = Hypotenuse × Cos

  x = 5·cos(Ф)