### 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.

*n*² +*n*² =*d*²

Solve for*d*.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

*k*

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?