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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. 

  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?