## Introduction

If you are a math student, you know how important special right triangles are in solving complex problems. The second worksheet on special right triangles is a comprehensive set of questions that tests your understanding of the concept. In this article, we will provide you with the answer key to the worksheet and explain how to solve each problem step-by-step.

## Problem 1

The first problem in the worksheet requires you to find the missing side lengths of a 45-45-90 triangle. This type of triangle is a special right triangle where the two legs are congruent and the hypotenuse is equal to the leg multiplied by the square root of 2. To find the missing side lengths, you simply need to use the Pythagorean theorem and the properties of the 45-45-90 triangle. The answer to this problem is (5, 5, 5√2).

## Problem 2

In problem 2, you are given a 30-60-90 triangle and you need to find the length of the missing side. This type of triangle is also a special right triangle, where the hypotenuse is twice the length of the shorter leg and the longer leg is equal to the shorter leg multiplied by the square root of 3. To solve this problem, you need to use the properties of the 30-60-90 triangle and the Pythagorean theorem. The answer to this problem is (√3, 1, 2).

## Problem 3

Problem 3 requires you to find the area of a 30-60-90 triangle. To find the area, you need to use the formula 1/2 * base * height. In this case, the base is the shorter leg and the height is the longer leg multiplied by the square root of 3. The answer to this problem is 15 square units.

## Problem 4

In problem 4, you are given a right triangle with the length of one leg and the hypotenuse. You need to find the length of the other leg. To solve this problem, you need to use the Pythagorean theorem and the fact that the triangle is a special right triangle. The answer to this problem is (√7, 2, √11).

## Problem 5

Problem 5 requires you to find the length of the hypotenuse of a 30-60-90 triangle. To solve this problem, you need to use the properties of the 30-60-90 triangle and the Pythagorean theorem. The answer to this problem is 4.

## Problem 6

In problem 6, you are given a right triangle with the length of one leg and the hypotenuse. You need to find the length of the other leg. To solve this problem, you need to use the Pythagorean theorem and the fact that the triangle is a special right triangle. The answer to this problem is (3, 4, 5).

## Problem 7

Problem 7 requires you to find the missing side lengths of a 45-45-90 triangle. To solve this problem, you need to use the properties of the 45-45-90 triangle and the Pythagorean theorem. The answer to this problem is (8, 8, 8√2).

## Problem 8

In problem 8, you are given a right triangle with the length of one leg and the hypotenuse. You need to find the length of the other leg. To solve this problem, you need to use the Pythagorean theorem and the fact that the triangle is a special right triangle. The answer to this problem is (√15, 2, √19).

## Problem 9

Problem 9 requires you to find the area of a 45-45-90 triangle. To solve this problem, you need to use the formula 1/2 * base * height. In this case, the base is one of the legs and the height is the same length. The answer to this problem is 32 square units.

## Problem 10

In problem 10, you are given a right triangle with the length of one leg and the hypotenuse. You need to find the length of the other leg. To solve this problem, you need to use the Pythagorean theorem and the fact that the triangle is a special right triangle. The answer to this problem is (4, 3, 5).

## Conclusion

Special right triangles are an essential concept in math, and the second worksheet on special right triangles is a great way to test your knowledge. In this article, we have provided you with the answer key to the worksheet and explained how to solve each problem. We hope that this article has helped you understand special right triangles better and has prepared you for any future math problems involving these triangles.

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