## Homework 2 Special Right Triangles Answer Key Introduction:

Are you struggling with your homework on special right triangles? Fear not, as we’re here to help you every step of the way! In this blog post, we’ll be providing a comprehensive look at the homework 2 answer key for special right triangles, providing all the necessary information you need to succeed. Whether you’re a high school student, a college student, or someone just looking to brush up on their geometry skills, this post is for you! So, let’s dive in and master those special right triangles once and for all!

### Blog Body:

Before we dive into the answer key, let’s review the basics of special right triangles. Special right triangles are two types of triangles that have specific angle and side ratios that make them easy to solve. The first type is the 45-45-90 triangle, which has two equal angles of 45 degrees and sides that are in a ratio of 1:1:√2. The second type is the 30-60-90 triangle, which has angles of 30 degrees, 60 degrees, and a right angle, and sides in the ratio of 1:√3:2.

Now, let’s take a look at the answer key for homework 2 on special right triangles. The first problem asks you to find the length of the hypotenuse of a 45-45-90 triangle with legs of length 5. According to the ratio for a 45-45-90 triangle, the length of the hypotenuse is 5√2. So, the answer to this problem is 5√2.

The second problem asks you to find the length of the longer leg of a 30-60-90 triangle with a hypotenuse of length 10. According to the ratio for a 30-60-90 triangle, the longer leg is √3 times the shorter leg. To find the shorter leg, we need to divide the hypotenuse by 2. So, the shorter leg is 10/2 = 5. Therefore, the longer leg is 5√3. The answer to this problem is 5√3.

The third problem asks you to find the length of the shorter leg of a 30-60-90 triangle with a hypotenuse of length 8. We know that the shorter leg is half the length of the hypotenuse, so it’s 8/2 = 4. The longer leg is √3 times the shorter leg, so it’s 4√3. The answer to this problem is 4.

The fourth problem asks you to find the length of the hypotenuse of a 30-60-90 triangle with a shorter leg of length 5. We know that the shorter leg is half the length of the hypotenuse, so the hypotenuse is 5/0.5 = 10. The longer leg is √3 times the shorter leg, so it’s 5√3. The answer to this problem is 10.

The fifth problem asks you to find the length of the shorter leg of a 45-45-90 triangle with a hypotenuse of length 10. According to the ratio for a 45-45-90 triangle, the length of each leg is 10/√2. So, the length of the shorter leg is 10/√2 = 5√2. The answer to this problem is 5√2.

### Conclusion:

Hopefully, this comprehensive look at the homework 2 answer key for special right triangles has helped you better understand the concepts and provided the necessary tools to tackle these problems with ease. Remember to review the ratios of special right triangles and practice solving problems to become a master in this geometry skill. Keep practicing and you’ll be sure to ace that next geometry test!