Question
In triangle QRT, angle Q measures 80 degrees and angle T measures 35 degrees. Which list shows the side lengths of the triangle in or Eder from greatest to least?
A. QT RT OR
B. RT OT OR
C. OT OR RT
D. RT OR OT
A. QT RT OR
B. RT OT OR
C. OT OR RT
D. RT OR OT
Answers
GPT-4o mini
To determine the side lengths of triangle QRT in order from greatest to least, we need to use the relationship between the angles and the opposite sides in a triangle.
1. **Identify the angles**:
- Angle Q = 80 degrees
- Angle T = 35 degrees
- To find angle R, we use the fact that the sum of the angles in a triangle is 180 degrees:
\[
\text{Angle R} = 180 - \text{Angle Q} - \text{Angle T} = 180 - 80 - 35 = 65 \text{ degrees}
\]
2. **Relate angles to sides**:
- The side opposite the largest angle is the longest, and the side opposite the smallest angle is the shortest.
- In triangle QRT:
- Angle Q (80 degrees) is opposite side RT.
- Angle R (65 degrees) is opposite side QT.
- Angle T (35 degrees) is opposite side OR.
3. **Order the sides**:
- RT is opposite the largest angle (80 degrees) and is the longest side.
- QT is opposite the second largest angle (65 degrees) and is the second longest side.
- OR is opposite the smallest angle (35 degrees) and is the shortest side.
Thus, the order from greatest to least side length is:
- RT (longest)
- QT (second longest)
- OR (shortest)
None of the options directly mention QT, but if QT is being referred to as OT in option A, that would make sense. Since RT is the longest, we have:
**Option A: QT, RT, OR**
Therefore, the side lengths in order from greatest to least are:
A. QT, RT, OR - is the correct answer.
If QT is not an option but referred to as OT, we need to reconsider the other answers provided.
Please clarify the options to ensure I'm providing the best help.
1. **Identify the angles**:
- Angle Q = 80 degrees
- Angle T = 35 degrees
- To find angle R, we use the fact that the sum of the angles in a triangle is 180 degrees:
\[
\text{Angle R} = 180 - \text{Angle Q} - \text{Angle T} = 180 - 80 - 35 = 65 \text{ degrees}
\]
2. **Relate angles to sides**:
- The side opposite the largest angle is the longest, and the side opposite the smallest angle is the shortest.
- In triangle QRT:
- Angle Q (80 degrees) is opposite side RT.
- Angle R (65 degrees) is opposite side QT.
- Angle T (35 degrees) is opposite side OR.
3. **Order the sides**:
- RT is opposite the largest angle (80 degrees) and is the longest side.
- QT is opposite the second largest angle (65 degrees) and is the second longest side.
- OR is opposite the smallest angle (35 degrees) and is the shortest side.
Thus, the order from greatest to least side length is:
- RT (longest)
- QT (second longest)
- OR (shortest)
None of the options directly mention QT, but if QT is being referred to as OT in option A, that would make sense. Since RT is the longest, we have:
**Option A: QT, RT, OR**
Therefore, the side lengths in order from greatest to least are:
A. QT, RT, OR - is the correct answer.
If QT is not an option but referred to as OT, we need to reconsider the other answers provided.
Please clarify the options to ensure I'm providing the best help.