Convert the angles of a triangle to radians.
α1=35∘41′55′′
 ,  α2=95∘31′18′′
 ,  α3=48∘46′47′′
 
Express your answers in radians to six significant figures separated by commas.

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.

Convert the angles of a triangle to radians. α1=35∘41′55′′, α2=95∘31′18′′, α3=48∘46′47′′. Express your answers in radians to six significant figures separated by commas.

Learn how to convert the angles of a triangle from degrees, minutes, and seconds to radians with precision up to six significant figures. This solution demonstrates the conversion process using trigonometric concepts and key formulas, suitable for students in Grades 10-12.

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