﻿ Special Right Triangles Worksheets
In these worksheets, students will learn to work with special right triangles.

#### Special Right Triangles are triangles whose angles are in a particular ratio (30°, 60°, 90° and 45°, 45°, 90°). You can find the right triangle's third side by using the Pythagorean Theorem. It will become more best when you already know the two sides. There are some triangles, such as 45-45-90 and 30-60-90 triangles. People usually find their ratios without using the Pythagorean Theorem each time. With such patterns, you can solve the special triangle's sides that are missing but, you must know at least the length of one side of the triangle. Suppose you have a 45-45-90 right triangle with two triangle's sides each one is 6 inches, and one is x inches. You will find the value of x. Special right triangle There are angles of the right triangle that are 30-60-90 and 45-45-90. This way, you will have Pythagorean triple triangles. 30-60-90 angle triangles Such triangles have ratios x, x√3,2x. Solve this by using the formula of Pythagorean Theorem, X2 + (x√3)2 = (2x)2 X2 + 3x2 = 4 x 2 = 4 x2 45-45-90 angles of triangles A 45-45-90 right angle triangle side has ratios x, x, x√2 Here, we will use Pythagorean Theorem, X2 + x2 = (x√2)2 = 2x2 = 2x2 Remember that the order of side ratios should be important x, x, x√2 as each of the triangle has the same angle. The smallest sides and angles are the same. You will consider the same rule for the largest values.

There are 18 worksheets in this set, divided into three sets of 6. In the first set, students will solve problems with a geometry emphasis. In the second set, students will solve problems with a trigonometry emphasis. In the third set, students will work with right triangles in general. A sound understanding of the basic principles of geometry and trigonometry is required in order for students to be successful with these worksheets. Students will find the value of the specified side or angle of a right triangle. This set of worksheets contains lessons, step-by-step solutions to sample problems, both simple and more complex problems, reviews, and quizzes. It also includes ample worksheets for students to practice independently. Most worksheets contain between eight and ten problems. When finished with this set of worksheets, students will be able to find the value of a specified part of a right triangle. These worksheets explain how to find the value of a specified part of a right triangle. Sample problems are solved and practice problems are provided.

# Special Right Triangles Worksheets

## Special Right Triangles (Geometry Emphasis) Lesson

This worksheet explains how to find a length or an angle of a right triangle. A sample problem is solved, and two practice problems are provided.

## Worksheet

Students will find the requested measurement value of a given right triangle. Ten problems are provided.

## Practice

The goal here is to lean more on the geometry that presents itself to help you solve these exercises.

## Review and Practice

The concept of how to find the requested measurements based on the given information about a right triangle is reviewed. A sample problem is solved. Six practice problems are provided.

## Quiz

Students will demonstrate their proficiency with working with special right triangles by using a geometrically emphasis with these problems.

## Check

This sheet is really helpful to understand where your students are with this skill.

## Special Right Triangles (Trigonometry Emphasis) Lesson

This worksheet explains how to find the requested measurement value of a special right triangle. A sample problem is solved, and two practice problems are provided.

## Worksheet

Students will find all these missing values by using their knowledge of trigonometry.

## Practice

Find the exact value of the following: cosec 60° + cot 30°+ sin 30°

## Review and Practice

The concept of how to find the requested measurement value of a special right triangle is reviewed. A sample problem is solved. Six practice problems are provided.

## Quiz

Students will demonstrate their proficiency with relying on their skills to solve these types of problems. Ten problems are provided.

## Check

Students will find the requested measurement value of a special right triangle. Three problems are provided, and space is included for students to copy the correct answer when given.

## Lesson

This worksheet explains how to solve this: : In a right triangle normal is 12 and the ,hypotenuse is 14. Find the value of opposite side?

## Work with Right Triangles Worksheet

We will apply our math skills to solve real world problems like: A tree in a back yard is to be cut down. The base of the tree from the house is 23 meters away, and the angle of elevation from the house to the top of the tree is 45.5 degrees. Could the tree hit the house when it is cut down?

## Practice

Example: A fisherman drops a boat anchor and pays out 93 meters of anchor rope. The rope makes an angle of depression of 59.5 degrees with the horizontal. Assuming a level bottom, how deep in the water?

## Review and Practice

The concept of how to find the value of a specified part of a right triangle is reviewed. A sample problem is solved. Six practice problems are provided.

## Quiz

Students will demonstrate their proficiency in finding the value using the concepts with have explored in this section. Ten problems are provided.

## Check

A great way to approach solving these problems.