The measure of one acute angle in a right triangle is 4 times the measure of the other acute angle. Write and solve a system of equations to find the measures of the acute angles of the triangle.

Question

Find the measures of the acute angles of the triangle.

Answer 1

If A is the right angle of the triangle, B and C would be the two acute angles of the triangles.

Let B angle is 4 times the C angle. We will have B = 4C (1)   since A is the right agle the two other angles

of the triangle will have the sum of 90 degrees. That is B + C = 90 (2). Solving the system of equations (1) and  (2) we have the solution. the (2) becomes 4C + C = 90  or 5C = 90 or C=90/5 = 18

from (2) we have B = 90 - C.  Then B = 90-18 =72 degrees.

72 = 4*18