Page 2: Advanced Special Right Triangle Problems and Real-World Applications

This page continues with more complex special right triangle problems and includes real-world applications.

Solutions for problems 15-20:

15. x = 14√3, y = 14, z = 14√2
16. x = 12√2, y = 12√6, z = 24
17. x = 26√3, y = 39, z = 39√2
18. x = 10√3, y = 20, z = 10√6
19. x = 14√5, y = 14√2, z = 14√3
20. x = 10√2, y = 20√3, z = 30

Example: In problem 17, for a 30-60-90 triangle with the longest side (z) equal to 39√2, we can find x by dividing z by 2√3, and y by dividing z by √2.

Problem 21 involves finding the perimeter of a triangle: P = 24√3

Problem 22 calculates the perimeter of a square: P = 56√2

Definition: The perimeter of a shape is the distance around its outer edge.

Problems 23 and 24 present real-world applications:

23. Length of loading ramps: 6.25 ft
24. Speed of baseball throw: 106.1 ft/sec

Highlight: These real-world problems demonstrate how special right triangle concepts can be applied to practical situations, such as construction and sports.

This page provides advanced practice for U7l2 special right triangles solutions worksheet and serves as a comprehensive Unit 7 Right Triangles and Trigonometry answer key, including applications that might appear in a Unit 7 Right Triangles and Trigonometry Homework 4 trigonometric Ratios and Finding Missing Sides exercise.

Page 1: Special Right Triangles Solutions

This page contains solutions for 14 problems involving special right triangles, primarily 30-60-90 and 45-45-90 triangles.

Highlight: The problems focus on finding the values of variables in special right triangles using their unique properties.

Solutions for selected problems:

1. x = 17, y = 17√3
2. x = 13√2, y = 13
3. x = 3√3, y = 6
4. x = 34, y = 17√3
5. x = 10√2, y = 10
6. x = 4√7, y = 8√7

Example: In problem 4, for a 30-60-90 triangle with hypotenuse 34, the shorter leg (x) is 34 ÷ 2 = 17, and the longer leg (y) is 17√3.

7. x = 2√7, y = 2√6
8. x = 15√2, y = 15√2
9. x = 18√3, y = 18
10. x = √6, y = √2
11. z = 24√3, y = 24
12. x = 16√3, y = 8√3
13. x = 13, y = 13√2
14. x = 4√7, y = 4√21

Vocabulary: Special right triangles are right triangles with specific angle measurements that have consistent side length ratios.

The solutions demonstrate the application of U7l2 special right triangles solutions concepts, providing a comprehensive Unit 7 Right triangles and Trigonometry Homework 1 answer key.