#### 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,
X^{2} + (x√3)^{2} = (2x)^{2}
X^{2} + 3x^{2} = 4 x ^{2} = 4 x^{2}
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,
X^{2} + x^{2} = (x√2)^{2} = 2x^{2} = 2x^{2}
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.