Find the angles of a right triangle if the difference of the acute angles is 24 degrees.

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academicsfirst's profile pic

academicsfirst | High School Teacher | (Level 2) Adjunct Educator

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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.

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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.

jc211's profile pic

jc211 | (Level 2) eNoter

Posted on

90, 57, and 24

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