Question

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 ∅ .

Answer 1

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Answer:

• x = √(25 -y²)
• x = 5cos(Ф)

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)