http://www.ck12.org Chapter 8. Right Triangle Trigonometry
8.4 45-45-90 Right Triangles
Here you’ll learn that the sides of a 45-45-90 right triangle are in the ratiox:x:x
√
2.
What if you were given an isosceles right triangle and the length of one of its sides? How could you figure out
the lengths of its other sides? After completing this Concept, you’ll be able to use the 45-45-90 Theorem to solve
problems like this one.
Watch This
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Click image to the left for more content.CK-12 Foundation: Chapter8454590RightTrianglesA
Watch the second half of this video.
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Click image to the left for more content.James Sousa:Trigonometric Function Values of Special Angles
Watch the second half of this video.
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Click image to the left for more content.James Sousa:SolvingSpecialRight Triangles
Guidance
There are two types of special right triangles, based on their angle measures. The first is an isosceles right triangle.
Here, the legs are congruent and, by the Base Angles Theorem, the base angles will also be congruent. Therefore,
the angle measures will be 90◦, 45 ◦,and 45◦. You will also hear an isosceles right triangle called a 45-45-90 triangle.
Because the three angles are always the same, all isosceles right triangles are similar.