Answer to Question #23507 in Analytic Geometry for arjay abainza

Question

one acute angle of a right triangle measures 10 degrees more than 3 times the measures of the other acute angle. what are the measures of the three angle

Answer 1

Let's denote the measures of the angles of the triangle by A, B and C. As the triangle is right, the measure of the third angle is C = 90°. The sum of the measures of the other two angles need to be

A + B = 180 - C = 180° - 90° = 90°, (1)

as the sum of all the angles of an arbitrary triangle is 180°. Also we know that

A - 10° = 3B (2).

So, we've got the system of equations (1), (2). Let's solve it:

(2) ==> A = 3B + 10°;

(1): A + B = 90° ==> 3B + 10° + B = 90° ==> 4B = 80° ==> B = 20°;

A = 3B + 10° = 3*20° + 10° = 70°.

So, the measures of the angles of the triangle are 20°, 70° and 90°.