Edexcel C2 — Question 2 6 marks

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSine and Cosine Rules
TypeTriangle area calculation
DifficultyModerate -0.3 This is a straightforward application of Heron's formula or the cosine rule followed by area = ½ab sin C. It requires only standard technique with no problem-solving insight, making it slightly easier than average, though the calculation steps prevent it from being trivial.
Spec1.05c Area of triangle: using 1/2 ab sin(C)
2. The sides of a triangle have lengths of \(7 \mathrm {~cm} , 8 \mathrm {~cm}\) and 10 cm . Find the area of the triangle correct to 3 significant figures.
AnswerMarks Guidance
\(10^2 = 7^2 + 8^2 - (2 \times 7 \times 8 \times \cos\theta)\)M1 A1
\(\cos\theta = \frac{49 + 64 - 100}{112} = \frac{13}{112}\)M1 A1
\(\theta = 83.335\)M1 A1
area \(= \frac{1}{2} \times 7 \times 8 \times \sin 83.335\)M1
\(= 27.8\) cm\(^2\) (3sf)A1 (6 marks) 
$10^2 = 7^2 + 8^2 - (2 \times 7 \times 8 \times \cos\theta)$ | M1 A1 |
$\cos\theta = \frac{49 + 64 - 100}{112} = \frac{13}{112}$ | M1 A1 |
$\theta = 83.335$ | M1 A1 |
area $= \frac{1}{2} \times 7 \times 8 \times \sin 83.335$ | M1 |
$= 27.8$ cm$^2$ (3sf) | A1 | (6 marks)
2. The sides of a triangle have lengths of $7 \mathrm {~cm} , 8 \mathrm {~cm}$ and 10 cm .

Find the area of the triangle correct to 3 significant figures.\\

\hfill \mbox{\textit{Edexcel C2  Q2 [6]}}
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