Introduction:
Welcome to our comprehensive guide on the answer key for Homework 2, focusing on special right triangles. In this article, we will delve into the concept of special right triangles, explore their unique properties, and provide a step-by-step breakdown of the answer key. So, let's dive in and unlock the secrets of geometry!
Understanding Special Right Triangles:
Special right triangles are a fascinating aspect of geometry that offer shortcuts and patterns to solve complex problems. There are two types of special right triangles: the 45-45-90 triangle and the 30-60-90 triangle. These triangles possess distinct angles and side ratios that make them special and easily solvable.
The 45-45-90 Triangle:
The 45-45-90 triangle is an isosceles right triangle, meaning it has two equal angles of 45 degrees each and two equal sides. The third angle in this triangle is always 90 degrees. The side ratios in a 45-45-90 triangle are as follows:
- The length of the two equal legs is represented by x.
- The length of the hypotenuse is √2 times the length of the legs.
To further illustrate this concept, let's consider an example from Homework 2:
Question 1: Find the value of x in the 45-45-90 triangle, where the hypotenuse is 10 units.
Solution: Using the side ratio, we know that x = 10/√2. Simplifying this equation, we find that x ≈ 7.07 units.
The 30-60-90 Triangle:
The 30-60-90 triangle is another special right triangle with angles measuring 30, 60, and 90 degrees. In this triangle, the side ratios are as follows:
- The length of the shorter leg (opposite the 30-degree angle) is represented by x.
- The length of the longer leg (opposite the 60-degree angle) is √3 times the length of the shorter leg.
- The length of the hypotenuse is 2 times the length of the shorter leg.
Let's tackle another question from Homework 2 to solidify our understanding:
Question 2: Determine the value of x in the 30-60-90 triangle, where the hypotenuse is 12 units.
Solution: Using the side ratio, we have x = 12/2. Simplifying this equation, we find that x = 6 units.
Conclusion:
In conclusion, special right triangles provide us with elegant solutions to geometric problems, making them invaluable tools for mathematicians. By understanding the side ratios and properties of 45-45-90 and 30-60-90 triangles, we can confidently solve complex equations. We hope this article has shed light on the answer key for Homework 2, helping you unlock the secrets of special right triangles.
FAQs (Frequently Asked Questions):
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Are special right triangles only applicable to Homework 2? No, special right triangles are a fundamental concept in geometry that can be applied to various mathematical problems.
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Can special right triangles be used to solve real-world problems? Absolutely! Special right triangles find applications in fields such as architecture, engineering, and physics, where precise calculations are necessary.
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Are there any other types of special triangles apart from the 45-45-90 and 30-60-90 triangles? Yes, there are other special triangles like the 36-72-72 triangle and the 18-72-90 triangle. However, the 45-45-90 and 30-60-90 triangles are the most commonly encountered in geometry.
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Is it possible for a triangle to be both a 45-45-90 and a 30-60-90 triangle simultaneously? No, a triangle can only be classified as either a 45-45-90 or a 30-60-90 triangle based on its angle measurements.
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Can special right triangles be used in trigonometry? Absolutely! Special right triangles serve as a foundation for trigonometric functions such as sine, cosine, and tangent.
Remember, understanding special right triangles is not only essential for acing your homework but also for building a strong foundation in geometry. Keep practicing and exploring the wonders of mathematics!
1. [PDF] Special Right Triangles
7.2 Homework. Solve using the Pythagorean Theorem. 2) x = 1) x = 5. 5. Name: Period: 2√5. 3) x = Answer key. 4) x = Algebra II DEAL. 3NZ. 4. 3. X. 13. 12. 2. 3.
2. [PDF] Special Right Triangles Homework Solutions #1-32
60° x=713 y=14. Label each special right triangle, and find the missing sides. 1 ... 2,3√2 212,912 02/22/2. © 2010 www.letspracticegeometry.com. 09,9. Page 4. 23 ...
3. [PDF] Special Right Triangles Worksheet #2
Special Right Triangles Worksheet #2. ANSWER KEY. 1. 8. 45'. 8√2. 4. 913. 1301. 9 ... 14 The length of one side of an equilateral triangle is 6 √3 meters. Find ...
4. 7.3 Special Right Triangles II - Flipped Math - Geometry
Section 7.3 Special Right Triangles II · More videos on YouTube · Packet · Practice Solutions · Corrective Assignment · Application Walkthrough · Leave any comments, ...
G.2.5: Explain and use angle and side relationships in problems with special right triangles, such as 30°, 60°, and 90° triangles and 45°, 45°, and 90° triangles.
5. [PDF] NAME
Find x. 1. X=25√2. 4. Special Right Triangles.
6. [PDF] Kuta Software - Infinite Geometry - Special Right Triangles
Find the missing side lengths. Leave your answers as radicals in simplest form. 1) b. 45°. 2√2 a. 6=a. 6=2√2. C = a√Z. C=2√2.√Z.
7. Special Right Triangles Lesson by Mrs E Teaches Math - TPT
Homework - The homework is 2 pages. Challenge Worksheet - The challenge ... Answer Key. Included. Teaching Duration. 50 minutes. Report this resource to TPT.
This NO PREP lesson teaches students about special right triangles. Students will learn all the rules for 45-45-90 triangles and 30-60-90 triangles. Differentiation and homework are included!Included:Warm-Up - The warm-up is a review of similar right triangles and simplifying radicals.Guided Notes...
8. Special Right Triangles: 45-45-90 Practice Worksheet - TPT
... 2. Resource Type. Worksheets, Homework. Formats Included. PDF. Pages. 4 pages. $2.00 ... Answer Key. Included. Teaching Duration. 30 minutes. Report this resource ...
The best way for students understand and memorize the rules for special right triangles is practice, practice, practice. As they say, practice make permanent! This worksheet could be used as a homework assignment or even a quiz over 45-45-90 triangles only. All answers are required to be in simpl...
