Moderate -0.8 This is a straightforward sine rule application requiring students to find an angle using the sine rule, then use angle sum to find the largest angle. It's a standard textbook exercise with clear setup and routine calculation, making it easier than average but not trivial since it requires recognizing that the largest angle is opposite the longest side and careful application of the sine rule.
4
The diagram shows a triangle \(A B C\).
\(A B\) is the shortest side. The lengths of \(A C\) and \(B C\) are 6.1 cm and 8.7 cm respectively.
The size of angle \(A B C\) is \(38 ^ { \circ }\)
Find the size of the largest angle.
Give your answer to the nearest degree.
\includegraphics[max width=\textwidth, alt={}, center]{ad6590e8-6673-45ca-bef3-a14716978827-05_2488_1716_219_153}
Uses the sine rule, or substitutes correctly into the cosine rule
\(A = 180 - 61.4 = 118.58... = 119°\)
A1
Obtains a value of 61 or 61.410964... rounded or truncated; condone answer in radians of 1.0718... or 0.4364...; PI by correct obtuse angle or 81. Or obtains correct length \(AB = 3.9367...\) or \(AB^2 = 15.4998...\)
Largest angle is \(119°\)
A1
Deduces the largest angle is 119; AWRT; CAO
## Question 4:
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{\sin\theta}{8.7} = \frac{\sin 38}{6.1}$, giving $\theta = 61.4$ | M1 | Uses the sine rule, or substitutes correctly into the cosine rule |
| $A = 180 - 61.4 = 118.58... = 119°$ | A1 | Obtains a value of 61 or 61.410964... rounded or truncated; condone answer in radians of 1.0718... or 0.4364...; PI by correct obtuse angle or 81. Or obtains correct length $AB = 3.9367...$ or $AB^2 = 15.4998...$ |
| Largest angle is $119°$ | A1 | Deduces the largest angle is 119; AWRT; CAO |
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4
The diagram shows a triangle $A B C$.\\
$A B$ is the shortest side. The lengths of $A C$ and $B C$ are 6.1 cm and 8.7 cm respectively.
The size of angle $A B C$ is $38 ^ { \circ }$\\
Find the size of the largest angle.\\
Give your answer to the nearest degree.\\
\includegraphics[max width=\textwidth, alt={}, center]{ad6590e8-6673-45ca-bef3-a14716978827-05_2488_1716_219_153}
\hfill \mbox{\textit{AQA Paper 2 2022 Q4 [3]}}