### 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.

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.

Solve for.What is the measure of the angle labeled

?What do you know about the interior angles of squares?

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

Use the Pythagorean Theorem to write an equation and solve for*k*.What is the measure of the angle labeled

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