To convert the angles of a triangle from degrees, minutes, and seconds to radians, we'll follow these steps:

1. Convert each angle from degrees, minutes, and seconds to decimal degrees.
2. Convert the decimal degrees to radians.

Step 1: Convert to Decimal Degrees

• $\alpha_1 = 35^\circ 41' 55''$
  Decimal degrees:
  $35^\circ + \frac{41'}{60} + \frac{55''}{3600}$
• $\alpha_2 = 95^\circ 31' 18''$
  Decimal degrees:
  $95^\circ + \frac{31'}{60} + \frac{18''}{3600}$
• $\alpha_3 = 48^\circ 46' 47''$
  Decimal degrees:
  $48^\circ + \frac{46'}{60} + \frac{47''}{3600}$

Step 2: Convert Decimal Degrees to Radians

To convert from degrees to radians, we use the formula: $\text{radians} = \text{degrees} \times \frac{\pi}{180}$

Let's calculate each one.The angles of the triangle converted to radians are approximately:

$\alpha_1 = 0.623058 \, \text{radians}, \, \alpha_2 = 1.667168 \, \text{radians}, \, \alpha_3 = 0.851367 \, \text{radians}$

Would you like more details or have any questions?

Here are five related questions:

1. How do you convert radians back to degrees?
2. What is the sum of the angles in radians for any triangle?
3. Can radians be expressed as a multiple of $\pi$ instead of decimals?
4. What is the significance of using radians instead of degrees in trigonometry?
5. How would you solve a triangle if two angles and one side are given?

Tip: When working with trigonometric functions, using radians instead of degrees often simplifies the mathematics, especially in calculus.