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Home > PC3 > Chapter 1 > Lesson 1.3.1 > Problem 1-117

1-117.

Use the Pythagorean Theorem and the diagrams below to answer the following questions. 

Square with top & left sides labeled, n, with dashed diagonal from lower left to upper right vertex. Angle between diagonal & bottom side, labeled, x.

Triangle, with dashed segment from top vertex, perpendicular to bottom side, labeled, k, Each side of triangle labeled, 2, N. Bottom left angle labeled, y.

  1. The square at right has sides of length . What is the length of the diagonal in terms of ? Use exact values.

    Use the Pythagorean Theorem.
    n² + n² = d²
    Solve for d.

  2. What is the measure of the angle labeled ?

    What do you know about the interior angles of squares?

  3. The triangle at right is equilateral with each with sides of length . What is the height in terms of ? Use exact values.

    The base is made into two equal parts by k
    Use the Pythagorean Theorem to write an equation and solve for k.

  4. What is the measure of the angle labeled ?

    What do you know about the interior angles of an equilateral triangle?