SOLUTION: This is the question:
If one acute angle of a right triangle is twice as big as the other, then the one leg of the triangle is twice the other. (We have to answer Always, Someti
Algebra.Com
Question 173124: This is the question:
If one acute angle of a right triangle is twice as big as the other, then the one leg of the triangle is twice the other. (We have to answer Always, Sometimes, or never. If it is Sometimes or Never then we have to change it to make it an Always statement).
I know that it is Never but I can't find a triangle that makes it an Always statement. (We have to use GSP for this).
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If one acute angle of a right triangle is twice as big as the other, then the one leg of the triangle is twice the other. (We have to answer Always, Sometimes, or never. If it is Sometimes or Never then we have to change it to make it an Always statement).
----------------------------------
If one acute angle is twice the other, one is 30 degrees; the other is 60 degrees.
--------------
Then by the Law of Sines:
smaller/sin(30) = larger/sin(60)
---------------------------
Assume smaller is x and larger is 2x.
Then x/sin(30) = (2x)/sin(60)
--------------
Then x/(1/2) = (2x)/(sqrt(3/2)
Then 2x = 2x/(sqrt(2/3)
--------------------------
This can only be true if x = 0
---------------------------
But x cannot be zero if it is an acute angle.
-----------------------------
Therefore the assumption is wrong.
The sides opposite two complementary angles that are 2:1 cannot be 2:1.
===========================================================
Cheers,
Stan H.
RELATED QUESTIONS
This is a geometric question. The question is: in a right angle triangle, one acute angle (answered by richard1234)
in a right angle triangle, one acute angle is twice as big as the other acute angle. Find (answered by cleomenius)
In a right triangle, one of the acute angles is twice as large as the other acute angle.... (answered by math-vortex)
I am having problems with this question.
If one of the acute angles of a right... (answered by Fombitz)
in a right triangle, one angle is twice as big as the other angle. what are the two... (answered by Alan3354)
If one leg of a right triangle is 3 times as long as the other leg, what is the measure... (answered by Aldorozos,stanbon)
In a right triangle, one of the acute angles is 2 times as large as the other acute... (answered by Paul)
In a right triangle, one of the acute angles is 2 times as large as the other acute... (answered by josmiceli)
In a right triangle, one of the acute angles is fourteen times as large as the other... (answered by checkley77)