Question 1010163: In a right angled triangle, the two acute angles are in the ratio 2:1. Find the angles of the triangle
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! in a right triangle, the sum of the two acute angles will always be 90 degrees.
if the angles are in a ratio of 2:1, this means that they will always be in the ratio of 2x/1x regardless of the value of x.
if x = 1, then they are in the ratio of 2/1.
if x = 2, then they are in the ratio of 4/2 which simplifies to 2/1.
if x = 3, then they are in the ratio of 6/3 which simplifies to 2/1.
if they are in the ratio of 2x/1x then their sum will be 2x + 1x = 3x.
you get 3x = 90 and solve for x to get x = 30
when x = 30, 2x = 60 and x = 30
your two acute angles are 60 degrees and 30 degrees.
their sum is 90 degrees.
the right angle is 90 degrees.
the sum of the angles of any triangle is 180 degrees.
90 + 90 = 180 so you're good.
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