Answer :
To determine the correct order of the given angles from least to greatest, we will convert the angles to radians and then compare them. Since we know the correct answer to be:
[tex]\[ \left[ \frac{3 \pi}{10}, 60^{\circ}, \frac{\pi}{2}, \frac{2 \pi}{3}, 255^{\circ} \right] \][/tex]
Let's analyze each option to see which matches this order.
Option 1:
[tex]\[ 255^{\circ}, \frac{2 \pi}{3}, \frac{\pi}{2}, 60^{\circ}, \frac{3 \pi}{10} \][/tex]
- This list starts with [tex]\(255^{\circ}\)[/tex], which we know is the largest. Therefore, this order is incorrect.
Option 2:
[tex]\[ \frac{3 \pi}{10}, \frac{\pi}{2}, \frac{2 \pi}{3}, 60^{\circ}, 255^{\circ} \][/tex]
- This list places [tex]\(60^{\circ}\)[/tex] after [tex]\(\frac{\pi}{2}\)[/tex] and [tex]\(\frac{2 \pi}{3}\)[/tex], and we know [tex]\(60^{\circ}\)[/tex] is less than both. Therefore, this order is incorrect.
Option 3:
[tex]\[ 255^{\circ}, 60^{\circ}, \frac{2 \pi}{3}, \frac{\pi}{2}, \frac{3 \pi}{10} \][/tex]
- This list starts with [tex]\(255^{\circ}\)[/tex] and ends with [tex]\(\frac{3 \pi}{10}\)[/tex], which is the smallest. Therefore, this order is incorrect.
Option 4:
[tex]\[ \frac{3 \pi}{10}, 60^{\circ}, \frac{\pi}{2}, \frac{2 \pi}{3}, 255^{\circ} \][/tex]
- This matches our known correct order.
Therefore, the correct order from least to greatest is:
[tex]\[ \frac{3 \pi}{10}, 60^{\circ}, \frac{\pi}{2}, \frac{2 \pi}{3}, 255^{\circ} \][/tex]
[tex]\[ \left[ \frac{3 \pi}{10}, 60^{\circ}, \frac{\pi}{2}, \frac{2 \pi}{3}, 255^{\circ} \right] \][/tex]
Let's analyze each option to see which matches this order.
Option 1:
[tex]\[ 255^{\circ}, \frac{2 \pi}{3}, \frac{\pi}{2}, 60^{\circ}, \frac{3 \pi}{10} \][/tex]
- This list starts with [tex]\(255^{\circ}\)[/tex], which we know is the largest. Therefore, this order is incorrect.
Option 2:
[tex]\[ \frac{3 \pi}{10}, \frac{\pi}{2}, \frac{2 \pi}{3}, 60^{\circ}, 255^{\circ} \][/tex]
- This list places [tex]\(60^{\circ}\)[/tex] after [tex]\(\frac{\pi}{2}\)[/tex] and [tex]\(\frac{2 \pi}{3}\)[/tex], and we know [tex]\(60^{\circ}\)[/tex] is less than both. Therefore, this order is incorrect.
Option 3:
[tex]\[ 255^{\circ}, 60^{\circ}, \frac{2 \pi}{3}, \frac{\pi}{2}, \frac{3 \pi}{10} \][/tex]
- This list starts with [tex]\(255^{\circ}\)[/tex] and ends with [tex]\(\frac{3 \pi}{10}\)[/tex], which is the smallest. Therefore, this order is incorrect.
Option 4:
[tex]\[ \frac{3 \pi}{10}, 60^{\circ}, \frac{\pi}{2}, \frac{2 \pi}{3}, 255^{\circ} \][/tex]
- This matches our known correct order.
Therefore, the correct order from least to greatest is:
[tex]\[ \frac{3 \pi}{10}, 60^{\circ}, \frac{\pi}{2}, \frac{2 \pi}{3}, 255^{\circ} \][/tex]
