Question
Error analysis
Small square inside the top of triangle
40
x◤
60
tan (60) =40/x
x • tan (60) 40/x (cross out) • x (cross out)
x • tan (60)/ tan (60) (cross out) = 40/tan (60)
x= 23.1
Did the student use the correct trigonometric function?
A. Yes
B. No
What function should the student use?
You must select ONE correct answer.
A. Sine
B. Cosine
C. The student used the correct trigonometric function
What’s the correct answer
A. x= 34.6
B. x= 69.3
C. x= 23.1
D. x= 46.2
Small square inside the top of triangle
40
x◤
60
tan (60) =40/x
x • tan (60) 40/x (cross out) • x (cross out)
x • tan (60)/ tan (60) (cross out) = 40/tan (60)
x= 23.1
Did the student use the correct trigonometric function?
A. Yes
B. No
What function should the student use?
You must select ONE correct answer.
A. Sine
B. Cosine
C. The student used the correct trigonometric function
What’s the correct answer
A. x= 34.6
B. x= 69.3
C. x= 23.1
D. x= 46.2
Answers
GPT-4o mini
To determine whether the student used the correct trigonometric function and to find the correct answer, let's analyze the problem step by step based on the given information.
1. **Understanding the Trigonometric Context**:
- The setup describes a triangle with a small square (likely representing some relationship or height) and is associated with angles of 40 degrees and 60 degrees.
- The student used the tangent function: \( \tan(60^\circ) = \frac{40}{x} \).
2. **Checking the Correct Trigonometric Function**:
- The tangent function relates the opposite side to the adjacent side in a right triangle.
- Given the description, if 40 represents the side opposite the 60-degree angle and \( x \) represents the adjacent side, the student chose appropriately by using tangent.
- Therefore, the student's choice was correct.
3. **Finding the Correct Value for \( x \)**:
- The student set up the equation correctly: \( x \cdot \tan(60^\circ) = 40 \).
- Rearranging gives:
\[
x = \frac{40}{\tan(60^\circ)}
\]
- The value of \( \tan(60^\circ) \) is \( \sqrt{3} \) or approximately \( 1.732 \). Thus:
\[
x \approx \frac{40}{1.732} \approx 23.1
\]
4. **Identifying the Correct Answer**:
- The calculation made by the student, \( x = 23.1 \), is indeed correct based on using the tangent function properly. However, let's verify the answer options given:
- A. \( x = 34.6 \)
- B. \( x = 69.3 \)
- C. \( x = 23.1 \)
- D. \( x = 46.2 \)
Based on the analysis:
1. **Did the student use the correct trigonometric function?**
- **Answer**: A. Yes
2. **What function should the student use?**
- **Answer**: C. The student used the correct trigonometric function
3. **What's the correct answer?**
- **Answer**: C. \( x = 23.1 \)
Therefore, all analyses confirm that the student was correct in their method and results.
1. **Understanding the Trigonometric Context**:
- The setup describes a triangle with a small square (likely representing some relationship or height) and is associated with angles of 40 degrees and 60 degrees.
- The student used the tangent function: \( \tan(60^\circ) = \frac{40}{x} \).
2. **Checking the Correct Trigonometric Function**:
- The tangent function relates the opposite side to the adjacent side in a right triangle.
- Given the description, if 40 represents the side opposite the 60-degree angle and \( x \) represents the adjacent side, the student chose appropriately by using tangent.
- Therefore, the student's choice was correct.
3. **Finding the Correct Value for \( x \)**:
- The student set up the equation correctly: \( x \cdot \tan(60^\circ) = 40 \).
- Rearranging gives:
\[
x = \frac{40}{\tan(60^\circ)}
\]
- The value of \( \tan(60^\circ) \) is \( \sqrt{3} \) or approximately \( 1.732 \). Thus:
\[
x \approx \frac{40}{1.732} \approx 23.1
\]
4. **Identifying the Correct Answer**:
- The calculation made by the student, \( x = 23.1 \), is indeed correct based on using the tangent function properly. However, let's verify the answer options given:
- A. \( x = 34.6 \)
- B. \( x = 69.3 \)
- C. \( x = 23.1 \)
- D. \( x = 46.2 \)
Based on the analysis:
1. **Did the student use the correct trigonometric function?**
- **Answer**: A. Yes
2. **What function should the student use?**
- **Answer**: C. The student used the correct trigonometric function
3. **What's the correct answer?**
- **Answer**: C. \( x = 23.1 \)
Therefore, all analyses confirm that the student was correct in their method and results.