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A 30o-60o-right triangle is half of what other kind of triangle?
90
Which is the 30o-60o-right triangle theorem?
If its a 300-600-right angle triangle then the third angle must be 90 degrees. Then its base squared plus its height squared equals its hypotenuse squared usually written in the form of: a2+b2 = c2
Are all the sides of a right triangle congruent?
Certainly not. In an equilateral triangle, in which all sides and all angles are congruent (or in other words, are the same) then all angles are 60o angles, there is no 90o angle and therefore it is not a right triangle. A typical right triangle would have angles of 90o, 60o, and 30o, and each of the three sides would be a different length.
How much degrees is a right angle triangle?
The angles of a triangle always add up to 180o. A right angle triangle has angle of 90o, 60o, 60o.
Why is the long leg the square root of 3 times bigger then the short leg in a 30 60 90 triangle?
I guess you are asking of the two sides which are not the hypotenuse, why the longer is root 3 times the shorter. Consider a 30, 60, 90 triangle ABC with ∠A = 30o, ∠B = 90o and ∠C = 60o and so side AC is the hypotenuse and BC is the shortest side. Reflect the triangle ABC in side BC to create triangle ABE. ∠EAB will be 30o, ∠ABE 90o and ∠BEA 60o. Side AE = AC. ∠EAC = ∠EAB + ∠BAC = 30o + 30o = 60o So triangle ACE is an equilateral triangle and thus side EC = AC Since EC = AC and EB = BC, EC=EB + BC ⇒ AC = BC + BC ⇒ AC = 2BC Using Pythagoras on triangle ABC to find length AB gives: AB2 + BC2 = AC2 ⇒ AB2 + BC2 = (2BC)2 ⇒ AB2 = 4BC2 - BC2 ⇒ AB2 = 3BC2 ⇒ AB = √3BC ie the shortest side is root 3 times the other non-hypotenuse side.
