Problem: The difference of the measures of two acute angles of a right angle triangle is 72°. Find the measures of the angles in radians.

Solution:

To solve this problem, we need to understand the properties of a right angle triangle and convert the angle measures from degrees to radians.

Step 1: Understand the properties of a right angle triangle

A right angle triangle is a triangle that contains one angle measuring 90°, called the right angle. The other two angles are acute angles, which means they measure less than 90°.

Step 2: Let's assume the measures of the two acute angles as x and y.

Let x be the larger angle and y be the smaller angle. According to the problem, the difference of the measures of these two angles is 72°. Therefore, we can write the equation:

x - y = 72°

Step 3: Convert the angle measures from degrees to radians.

To convert degrees to radians, we use the conversion factor: π radians = 180°. Therefore, 1° = π/180 radians.

Step 4: Convert the equation into radians.

Now, let's convert the equation x - y = 72° into radians.

x - y = 72°
(x - y) * (π/180) = 72 * (π/180)
(x - y) * (π/180) = π/5

Step 5: Simplify the equation.

To simplify the equation, let's multiply both sides by 180/π.

(x - y) = π/5 * (180/π)
(x - y) = 36

Step 6: Solve for x and y.

Since x - y = 36, we can substitute this value into the equation x - y = 72° to find the values of x and y.

x - y = 36
x - y = 72° (converting back to degrees)

Solving the equation, we find that x = 54° and y = 18°.

Step 7: Convert the angle measures back to radians.

Finally, let's convert the angle measures from degrees to radians.

x = 54° = 54 * (π/180) radians = 3π/10 radians
y = 18° = 18 * (π/180) radians = π/10 radians

Therefore, the measures of the two angles in radians are x = 3π/10 radians and y = π/10 radians.

Let the angle be A and B A+B = 90 A- B = 72 therfore A= 81 , B = 9 A= 9pi/20, B= pi/20