# Special Right Triangles Worksheet Answer Key With Work

## Introduction

Are you struggling with special right triangles, and looking for a way to improve your understanding? One of the best ways to do that is by using a worksheet with answer key and work. In this article, we'll go over what special right triangles are, why they're important, and how you can use a worksheet to master them.

## What Are Special Right Triangles?

Special right triangles are a type of triangle that have specific angles and side lengths. The two types of special right triangles are 45-45-90 triangles and 30-60-90 triangles. In a 45-45-90 triangle, the two legs are congruent and the hypotenuse is √2 times the length of the legs. In a 30-60-90 triangle, the sides are in a ratio of 1:√3:2, with the hypotenuse being twice as long as the shorter leg.

## Why Are Special Right Triangles Important?

Special right triangles are important because they come up frequently in math and science, especially in geometry and trigonometry. They're also useful in real-world applications, such as engineering and architecture. Understanding special right triangles is essential if you want to excel in these fields.

## How to Use a Special Right Triangles Worksheet

Using a special right triangles worksheet is a great way to practice and reinforce your understanding of these important triangles. A good worksheet should include problems that cover both 45-45-90 and 30-60-90 triangles, and should provide step-by-step solutions with work. This will help you see how to approach and solve different types of problems.

### Step 1: Identify the Type of Triangle

The first step in solving a special right triangle problem is to identify what type of triangle you're dealing with. Look at the angles and side lengths to determine if it's a 45-45-90 triangle or a 30-60-90 triangle.

### Step 2: Use the Ratio

Once you've identified the type of triangle, use the appropriate ratio to solve for the missing side length. For a 45-45-90 triangle, use the ratio 1:1:√2. For a 30-60-90 triangle, use the ratio 1:√3:2.