Related Pages
Pythagorean Triples
Types Of Triangles
Area Of Triangles
More Geometry Lessons

The two special right triangles are as important to Trigonometry as arithmetic is to mathematics. On this page you will find the information you need to understand the relationships they have between their sides and angles, as well as plenty of practice helping you learn to apply those relationships to find missing information. Pythagorean Theorem and Special Right Triangles. Right Triangles. Special Right Triangles Warm Up. Special Right Triangles.

Divides the equilateral triangle into two -WULDQJOHV Let x be the height of the triangle. Use special right triangles to find the height, which is the longer side of D -WULDQJOH 7KHK SRWHQXVHRIWKLV -WULDQJOHLV WKH shorter leg is, which makes the height, which LVDSSURLPDWHO FP. The Math section of the SAT is full of special right triangles. The 5-12-13 triangle is a common triple. If you can recognize the triple pattern then you can easily calculate a missing side. Here is a list of the common triples associated with a 5 -12-13 right triangle.

Recognizing Special Right Triangles

Recognizing special right triangles can provide ashortcut when answering some geometry questions. A special right triangle is a right trianglewhose sides are in a particular ratio, called the Pythagorean Triples. Youcan also use the Pythagorean theorem', but if you can see thatit is a special triangle it can save you some calculations.

The following figures show some examples of special right triangles and Pythagorean Triples.Scroll down the page if you need more explanations about special right triangles, Pythagoreantriples, videos and worksheets.

What is a 45°-45°-90° Triangle?

A 45°-45°-90° triangle is a special right triangle whose angles are 45°,45° and 90°. The lengths of the sides of a 45°-45°-90°triangle are in the ratio of 1 : 1 : √2.

A right triangle with two sides of equal lengths must be a 45°-45°-90° triangle.

You can also recognize a 45°-45°-90° triangle by the angles. A right trianglewith a 45° angle must be a 45°-45°-90° special right triangle.

Side1 : Side2 : Hypotenuse = x : x : x√2

Example 1:
Find the length of the hypotenuse of a right triangle if the lengths ofthe other two sides are both 3 inches.

Solution:
Step 1:This is a right triangle with two equal sides so it must be a 45°-45°-90°triangle.

Step 2:You are given that the both the sides are 3. If the first and second value of the ratiox:x:x√2 is 3 then the length of the third side is 3√2.

Answer: The length of the hypotenuse is 3√2 inches.

Example 2:
Find the lengths of the other two sides of a right triangle if the length of the hypotenuseis 4√2 inches and one of the angles is 45°.

Solution:
Step 1:This is a right triangle with a 45°-45°-90° triangle.

You are given that the hypotenuse is 4√2. Ifthe third value of the ratio n:n:n√2 is 4√2 then the lengths ofthe other two sides must 4.

MiniTools Software Limited developed Minitool Partition Wizard as a manager for disks and partitions on your Windows computer. It serves other functions in the management of your hardware like space analysis and wiping the partitions. It has an extensive toolkit to deal with all the basic problems or enhancements necessary for your partitions for increased PC speed. Minitool partition wizard 12 free.

Answer: Thelengths of the two sides are both 4 inches.

What is a 30°-60°-90° Triangle?

Another type of special right triangles is the 30°-60°-90°triangle. This is right triangle whose angles are 30°-60°-90°.The lengths of the sides of a 30°-60°-90°triangle are in the ratio of 1 : √3 : 2.

Gcc expert 24 lx driver windows 10. You can also recognize a 30°-60°-90° triangle by the angles. As long asyou know that one of the angles in the right-angle triangle is either 30°or 60° then it must be a 30°-60°-90° special right triangle. Aright triangle with a 30° angle or 60° angle must be a30°-60°-90° special right triangle.

Side1 : Side2 : Hypotenuse = x : x√3 : 2x

Example 1:
Find the length of the hypotenuse of a right triangle if the lengths ofthe other two sides are 4 inches and 4&dadic;3 inches.

Solution:
Step 1:Test the ratio of the lengths to see if it fits the n:n√2:2n ratio.

4:4√3:? = x:x√3:2x

Step 2:Yes, it is a 30°-60°-90° triangle for x = 4

Step 3:Calculate the third side.

2x = 2 × 4 = 8

Answer: Thelength of the hypotenuse is 8 inches.

Example 2:
Find the lengths of the other two sides of a right triangle if thelength of the hypotenuse is 8 inches and one of the angles is 30°.

Solution:
Step 1:This is a right triangle with a 30° angleso it must be a 30°-60°-90° triangle.

You are given that the hypotenuse is 8.
Substituting 8 into the third value of the ratio x:x√3:2x, we get that 2x = 8 ⇒ x = 4.

Substituting x = 4 into the first and second value of the ratio we get that the other twosides are 4 and 4√3.

Answer:The lengths of the two sides are 4 inches and 4√3 inches.

Special Triangles - Important Angles - 30°, 45°, 60°
45°-45°-90° Triangles, 30°-60°-90° Triangles.

Show Video Lesson

Basic triangles you should know
The triangles are classified by side and by angle.

In this video you will learn:

3-4-5 triangles and similar triangles.
5-12-13 triangles and similar triangles.
45-45-90 right triangles.
30-60-90 triangles.
equilateral triangles.
relationship between equilateral and 30-60-90 triangles.

How to Solve Special Right Triangles?
When solving special right triangles,remember that a 30-60-90 triangle has a hypotenuse twice as longas one of the sides, and a 45-45-90 triangle has two equal sides.

Show Video Lesson

Special Right Triangles in Geometry
45-45-90 and 30-60-90 degree triangles.

Discuss two special right triangles, how to derive the formulas tofind the lengths of the sides of the triangles by knowing the lengthof one side, and a few examples using them.

Special Right Triangles Examples Step By Step

What are Pythagorean Triples?
Any group of 3 integer values that satisfies the equation:a² + b² = c² is called a Pythagorean Triple.Any triangle that has sides that form a Pythagorean Triple must be a right triangle.Some examples of Pythagorean Triple triangles are: 3-4-5 Triangles and 5-12-13 Triangles.

What is a 3-4-5 Triangle?
Radula perrottetii buy. A 3-4-5 triangle is right triangle whose lengths are in the ratioof 3:4:5. When you are given the lengths of two sides of a righttriangle, check the ratio of the lengths to see if it fits the3:4:5 ratio.

Side1 : Side2 : Hypotenuse = 3n : 4n : 5n

Example 1:
Find the length of the hypotenuse of aright triangle if the lengths of the other two sides are 6 inches and 8 inches.

Solution:
Step 1: Test the ratio of thelengths to see if it fits the 3n : 4n : 5n ratio.

6 : 8 : ? = 3(2) : 4(2) : ?

Step 2: Yes, it is a 3-4-5 triangle for n = 2.

Step 3: Calculate the third side.

5n = 5 × 2 = 10

Answer: The length of the hypotenuse is 10 inches.

Example 2:
Find the length of one side of a right triangle if the length of thehypotenuse is 15 inches and the length of the other side is 12 inches.

Recognizing Special Right Triangles

What is a 45°-45°-90° Triangle?

What is a 30°-60°-90° Triangle?

Special Right Triangles Examples Step By Step

Special Right Triangles Quiz