Problem Analysis #30

GPT-5.1 (high) · Run 1

9.32s
2,340 toks
Problem Statement

In triangle ABCABC, suppose that AB‾=5\overline{AB} = 5, AC‾=6\overline{AC} = 6, and

cos⁡(∠BAC)=−35.\cos(\angle BAC) = -\dfrac{3}{5}.

Compute the area of triangle ABCABC. [3 points]\

Ground Truth
12
Execution Trace
Reasoning Process

[THOUGHT] We know two sides AB = 5, AC = 6 and the cosine of the included angle A. The area formula is: Area = (1/2) * AB * AC * sin(A). We have cos(A) = -3/5, so we can use sin^2(A) = 1 - cos^2(A) to find sin(A), then compute the area. I’ll verify numerically in Python. [/THOUGHT] [PYTHON] import math

AB = 5 AC = 6 cosA = -3/5

sinA = math.sqrt(1 - cosA**2) # positive sine for angle between 0 and pi area = 0.5 * AB * AC * sinA print(area) [/PYTHON]

Tool Output
[PYTHON OUTPUT] 12.0 [/PYTHON OUTPUT]
Reasoning Process

[THOUGHT] Using the formula for area with two sides and included angle, the Python computation gives area = 12. I will report 12 as the final answer.

Area=12⋅5⋅6⋅sin⁡(∠BAC)=12\text{Area} = \frac12 \cdot 5 \cdot 6 \cdot \sin(\angle BAC) = 12

[/THOUGHT] 12\boxed{12}

Final Model Output
12

Comparative Analysis (P30) (Average across runs)

Avg Time Taken

K-EXAONE-236B-A23B
89.7
Gemini-3-Pro-Preview
39.2
Llama-VARCO-8B-Instruct
29.5
HCX-007(high)
23.9
EXAONE-4.0.1-32B (high)
21.1
Deepseek-V3.2
15.1
Solar-Pro-2 (31B)(high)
14.5
Claude-Opus-4.5
14.2
Kanana-2-30B-Thinking-2601
13.8
Kanana-2-30B-Thinking
13.1
GPT-5.1 (high)
9.3
Grok-4.1-fast
8.3
Solar-Open-100B
8.0
A.X-4.0 (72B)
8.0
K-EXAONE-236B-A23B
7.0
GPT-5.2 (high)
5.2

Avg Token Usage

K-EXAONE-236B-A23B
12,099
Kanana-2-30B-Thinking-2601
4,283
A.X-4.0 (72B)
3,968
Kanana-2-30B-Thinking
3,934
Solar-Pro-2 (31B)(high)
3,926
HCX-007(high)
3,594
Grok-4.1-fast
3,275
Solar-Open-100B
3,195
Gemini-3-Pro-Preview
3,159
Claude-Opus-4.5
3,138
K-EXAONE-236B-A23B
3,091
Deepseek-V3.2
2,443
GPT-5.1 (high)
2,340
GPT-5.2 (high)
2,301
Llama-VARCO-8B-Instruct
1,159
EXAONE-4.0.1-32B (high)
1,032