Special Right Triangles
30 60 90 and 45 45 90 Special Right Triangles
Although all right triangles have special features – trigonometric functions and the Pythagorean theorem . The most frequently studied right triangles , the special right triangles, are the 30, 60, 90 Triangles followed by the 45, 45, 90 triangles.
The 30, 60, 90 Special Right Triangle
The picture below illustrates the general formula for the 30, 60, 90 Triangle.
General Formula
Specific Examples
45, 45, 90 Special Right Triangle
Some Specific Examples
Practice Using Special Right Triangles
What is the value of z in the triangle below?
The 30$$^{\circ}$$ and 60$$^{\circ}$$ angles give this one away.
x = 6 2x =12 z = $$ x \sqrt{3} = 6\sqrt{3} $$
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30-60-90 Special Right Triangles
These lessons help Grade 8 students to learn about the 30-60-90 special right triangle.
Related Pages 45-45-90 Right Triangle Other Special Right Triangles More lessons for Grade 7 and Grade 8 Math Worksheets
30-60-90 Triangles
A 30-60-90 triangle is a special type of right triangle. What is special about 30-60-90 triangles is that the sides of the 30-60-90 triangle always have the same ratio. Therefore, if we are given one side we are able to easily find the other sides using the ratio of 1:2:√3. Another special right triangle is the 45-45-90 triangle.
The following diagram shows the properties of a 30-60-90 Triangle. Scroll down the page for more examples and solutions on how to solve 30-60-90 Triangles.
How to find the legs and hypotenuse in 30-60-90 triangles when given: the short leg, the long leg, or the hypotenuse.
Solve a 30-60-90 Right Triangle This video provides examples of how to solve a 30-60-90 triangle given the length of one side.
30-60-90 Triangle
Finding the Missing Side of 30-60-90 Triangle
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Using the technique in the model above, find the missing sides in this 30°-60°-90° right triangle. Hypotenuse = 12 Short =
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Special Right Triangles (30-60-90 and 45,45,90) triangles explained with formulas, examples and pictures.
Special Right Triangles Date_____ Period____ Find the missing side lengths. Leave your answers as radicals in simplest form. 1) a 2 2 b 45° 2) 4 x y 45° 3) x y 3 2 2 45° 4) x y 3 2 45° 5) 6 x y 45° 6) 2 6 y x 45° 7) 16 x y 60° 8) u v 2 30°-1-
Solve for a missing side in 45-45-90 and 30-60-90 special right triangles. Answers with radicals must be reduced and rationalized.
This is an introductory assignment on 30-60-90 right triangles. More detailed notes or examples can be written on the board or these can be the notes that you have students copy or go through.
One of the two special right triangles is called a 30-60-90 triangle, after its three angles. 30-60-90 Theorem: If a triangle has angle measures 30 ∘, 60 ∘ and 90 ∘, then the sides are in the ratio x: x 3: 2 x. The shorter leg is always x, the longer leg is always x 3, and the hypotenuse is always 2 x. If you ever forget these theorems ...
The special nature of these triangles is their ability to yield exact answers instead of decimal approximations when dealing with trigonometric functions. This page will deal with the 30º-60º-90º triangle.
The following diagram shows the properties of a 30-60-90 Triangle. Scroll down the page for more examples and solutions on how to solve 30-60-90 Triangles. How to find the legs and hypotenuse in 30-60-90 triangles when given: the short leg, the long leg, or the hypotenuse.
In this lesson, you refreshed your knowledge on the three different types of triangles, found the properties of 45 45 90 and 30 60 90 triangles, and learned why they are called special right triangles.