The difference between the two acute angles of a right triangleis `(pi/3)^(c )`.
Find these angles in radians and degrees.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the relationship between the angles
In a right triangle, the sum of the two acute angles (let's call them angle A and angle B) is always 90 degrees (or π/2 radians). We are given that the difference between these two angles is π/3 radians.

### Step 2: Set up the equations
We can express the two angles using the following equations:
1. \( A + B = \frac{\pi}{2} \) (Equation 1)
2. \( A - B = \frac{\pi}{3} \) (Equation 2)

### Step 3: Solve the equations
To find the values of A and B, we can add Equation 1 and Equation 2:
\[ (A + B) + (A - B) = \frac{\pi}{2} + \frac{\pi}{3} \]
This simplifies to:
\[ 2A = \frac{\pi}{2} + \frac{\pi}{3} \]

### Step 4: Find a common denominator
The common denominator for 2 and 3 is 6. Therefore, we convert the fractions:
\[ \frac{\pi}{2} = \frac{3\pi}{6}, \quad \frac{\pi}{3} = \frac{2\pi}{6} \]
Now we can add them:
\[ 2A = \frac{3\pi}{6} + \frac{2\pi}{6} = \frac{5\pi}{6} \]

### Step 5: Solve for angle A
Now, divide both sides by 2 to find angle A:
\[ A = \frac{5\pi}{12} \]

### Step 6: Find angle B
Now we can substitute the value of A back into Equation 1 to find angle B:
\[ A + B = \frac{\pi}{2} \]
Substituting A:
\[ \frac{5\pi}{12} + B = \frac{\pi}{2} \]
Convert \(\frac{\pi}{2}\) to have a common denominator of 12:
\[ \frac{\pi}{2} = \frac{6\pi}{12} \]
Now solve for B:
\[ B = \frac{6\pi}{12} - \frac{5\pi}{12} = \frac{\pi}{12} \]

### Step 7: Convert angles to degrees
To convert the angles from radians to degrees, we use the conversion factor \( \frac{180}{\pi} \):
- For angle A:
\[ A = \frac{5\pi}{12} \times \frac{180}{\pi} = \frac{5 \times 180}{12} = 75^\circ \]
- For angle B:
\[ B = \frac{\pi}{12} \times \frac{180}{\pi} = \frac{180}{12} = 15^\circ \]

### Final Result
The two acute angles of the right triangle are:
- Angle A: \( \frac{5\pi}{12} \) radians or \( 75^\circ \)
- Angle B: \( \frac{\pi}{12} \) radians or \( 15^\circ \)