Convert the angles of a triangle to radians. 88∘45′21′′

To convert an angle from degrees, minutes, and seconds (DMS) into radians, follow these steps:

1. **Convert the minutes and seconds to decimal degrees:**
   - \( 88^\circ \) remains the same.
   - Convert the minutes to decimal degrees: \( \frac{45'}{60} = 0.75^\circ \).
   - Convert the seconds to decimal degrees: \( \frac{21''}{3600} \approx 0.00583^\circ \).

   Now, sum the values:
   \[
   88^\circ + 0.75^\circ + 0.00583^\circ = 88.75583^\circ
   \]

2. **Convert the decimal degrees to radians:**
   - Use the formula:
   \[
   \text{radians} = \text{degrees} \times \frac{\pi}{180}
   \]
   Substituting:
   \[
   88.75583^\circ \times \frac{\pi}{180} \approx 1.5483 \, \text{radians}
   \]

Thus, the angle \( 88^\circ 45' 21'' \) is approximately **1.5483 radians**.

Would you like more details on the process or help with another angle?

Here are some related questions:
1. How do you convert radians back to degrees?
2. What is the significance of radians in trigonometry?
3. How do you handle angles larger than 360 degrees?
4. Can you explain the unit circle and its relation to radians?
5. How do you calculate angles in different quadrants using radians?

**Tip:** Always keep your calculator in the correct mode (degree or radian) depending on the type of angle calculations you're performing!

Learn how to convert angles from degrees, minutes, and seconds to radians step-by-step. This example covers converting 88 degrees 45 minutes 21 seconds to radians using the appropriate conversion formulas. Suitable for high school students studying trigonometry.

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