Algebra/Chapter 14/Exercises

A set of exercises related to concepts from Chapter 14. This set contains 14 exercises (0 Conceptual Questions + 14 Exercises + 0 Projects) Conceptual Questions Exercises Section 14.1 (★) 14.1 (Pythagorean Triples) Determine if the following sets of numbers are Pythagorean Triples. 1. (5, 12, 13) 2. (9, 60, 61) (★) 14.2 (Using the Pythagorean Theorem) Find the missing lengths of the following right triangles. (★) 14.3 (Diagonal of a Square) What is the length of the diagonal of a square whose side length is: 1. 2 2. 3 3. 4 4. 5 5. r (★) 14.4 (Diagonal of a Rectangle) What is the length of the diagonal of a rectangle whose side lengths are: 1. 1 and 2 2. 3 and 5 3. 4 and 7 4. r and 2r 5. 3r and 5r 6. 4r and 7r (★★) 14.5 (Diagonal of a Cube) What is the length of the diagonal of a cube whose side length is: 1. 2 2. 3 3. 4 4. 5 5. r (★★) 14.6 (Diagonal of a Rectangular Prism) What is the length of the diagonal of a rectangular prism whose side lengths are: (★★) 14.7 (Diagonal of a Rectangular Prism II) What is the length of the diagonal of a rectangular prism whose side lengths are a, b, and c? What if the side lengths were ra, rb, and rc instead? (★★) 14.8 (Using the Pythagorean Theorem) A right triangle has the side lengths , , and . Find . (★★) 14.9 (Pencil Box) A pencil box, in the shape of a rectangular prism, measures 15 cm by 12 cm by 9 cm. Find the length of the longest pencil that can fit inside. (★★) 14.10 (Equilateral Triangle) Find the area of an equilateral triangle with 2 cm sides. (★★) 14.11 (Regular Hexagon) Find the area of a regular hexagon with 4 cm sides. (★★) *14.12 (Euclid's Formula) We can construct a set of Pythagorean Triples through a relation called Euclid's Formula. When we define m and n as positive integers, and m > n: Use the Pythagorean Theorem to prove Euclid's Formula. Section 14.2 (★) 14.13 (Right Triangle Trigonometry) Find the exact values of the six trigonometric functions of . Section 14.3 Section 14.4 Section 14.5 (★★) *14.14 (Sector Area) If , prove that . Section 14.6 Section 14.7 Section 14.8 Section 14.9 Section 14.10 Section 14.11 Section 14.12 Section 14.13 Reason and Apply Challenge Problems