SOLUTION: One of the angles of a right triangle is 25�. What is the ratio of the largest angle of the triangle to the difference between the acute angles?

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Question 1038901: One of the angles of a right triangle is 25�. What is the ratio of the largest angle of the triangle to the difference between the acute angles?
Answer by Theo(13342) (Show Source):
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the largest angle of a right triangle is 90 degrees.
the smallest angle is 25.
the other angle has to be 65 because the sum of the angle of any triangle is 180 degrees and 90 + 25 + 65 is equal to 180.

the difference between the acute angles is 65 - 25 = 40 degrees.
the ratio of the 90 degrees angle to the difference of 40 degrees is 90/40 = 9/4.

this makes the largest angle equal to 9/4 * the difference between the angles.

let a = 90 degrees.
let b = 40 degrees.

a is the largest angle.
b is the difference between the two smaller angles.

the ratio of a/b = 9/4.
multiply both sides of this equation by b to get a = 9/4 * b.
this means that the largest angle is equal to 9/4 times the difference.