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Find the angles of a right triangle if the difference of the acute angles is 24 degrees.
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The sum of all the angles of a triangle is 180 degrees. As the triangle being considered here is a right triangle, one of the angles is 90 degrees.
Let the other angles be A and B. The sum of these angles is A + B = 180 - 90 = 90
The difference of these angles is given as 24 degrees
=> A - B = 24
Substituting for B from A + B = 90
A - (90 - A) = 24
=> 2A - 90 = 24
=> 2A = 114
=> A = 57
The angles of the triangle are 33 degrees, 57 degrees and 90 degrees.
Posted by justaguide on May 3, 2011 at 12:07 PM (Answer #1)
High School Teacher
We are asked to find the angles of a right triangle given that the difference of the acute angles is 24 degrees.
There are 180 degrees in a right triangle.
A right triangle contains one 90 degree angle.
Let x = one acute angle
Let x + 24 = second acute angle
=> x + x + 24 + 90 = 180
=> 2x + 114 = 180
=> 2x = 66
=> x = 33 degrees
=> x + 24 = 57 degrees
The angles of the right triangle are 90 degrees, 57 degrees, and 33 degrees.
Posted by academicsfirst on May 3, 2011 at 8:02 PM (Answer #3)
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