Question 177436: Special Right Triangles:
Yes this a very general question. How do you find the length of the sides in 30-60-90 and 45-45-90 special right traingles? i'm completley lost. Thanks
Answer by edjones(8007)   (Show Source):
You can put this solution on YOUR website! 45-45-90 Isocoles right triangle. [1, 1, sqrt(2)]
Let a=1 and b=1
a^2+b^2=c^2
1+1=2
c=sqrt(2)
The sides of any isocoles right triangle are proportional to 1, 1, and sqrt(2)
Example: let the altitude be 7. The base is also 7. The hypotenuse is 7sqrt(2).
This rapid calculation is most helpful on SAT tests.
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30-60-90 [1, sqrt(3), 2]
cos(60)=1/2 which is the adj/hyp. Let the hypotenuse be 2 and the shorter side be 1. Tan(60)=sqrt(3)which is the length of the longer side.
The sides are, again proportional.
Example: Let the shortest side be 7. Then the hypotenuse is 7*2=14 and the longer side is 7sqrt(3)
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The 3-4-5 right triangle is the other triangle frequently found on SAT tests.
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Memorize the sides of these triangles and make your life easier.
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Ed
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