GCSE Edexcel Maths Forming & Solving Equations: Here is triangle ABC. (a) Find

Here is triangle ABC - Edexcel - GCSE Maths - Question 16 - 2021 - Paper 2

Question 16

Here is triangle ABC. (a) Find the length of BC. Give your answer correct to 3 significant figures. (b) Find the area of triangle ABC. Give your answer correct to ... show full transcript

Worked Solution & Example Answer:Here is triangle ABC - Edexcel - GCSE Maths - Question 16 - 2021 - Paper 2

Step 1

Find the length of BC.

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Answer

To find the length of side BC in triangle ABC, we can use the Law of Cosines. The formula is given by:

$c^2 = a^2 + b^2 - 2ab \cdot \cos(C)$

Where:

$a = 8$ cm (length of side AC)
$b = 11$ cm (length of side AB)
$C = 72°$ (angle at A)

Plugging in the values:

$BC^2 = 8^2 + 11^2 - 2 \cdot 8 \cdot 11 \cdot \cos(72°)$

Calculating each term:

$8^2 = 64$
$11^2 = 121$
$2 \cdot 8 \cdot 11 \cdot \cos(72°) \approx 2 \cdot 8 \cdot 11 \cdot 0.309 = 50.016$ approximately.

Thus:

$BC^2 = 64 + 121 - 50.016 = 134.984$

Taking the square root:

$BC = \sqrt{134.984} \approx 11.6 \text{ cm}$

Rounding to three significant figures gives:

$BC \approx 11.4$ cm.

Step 2

Find the area of triangle ABC.

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Answer

The area of triangle ABC can be calculated using the formula:

$\text{Area} = \frac{1}{2} \times a \times b \times \sin(C)$

Where:

$a = 8$ cm
$b = 11$ cm
$C = 72°$

Plugging in the values:

$\text{Area} = \frac{1}{2} \times 8 \times 11 \times \sin(72°)$

Calculating:

$\sin(72°) \approx 0.95106$ (using a calculator)

Thus:

$\text{Area} = \frac{1}{2} \times 8 \times 11 \times 0.95106 \approx 33.1574$

Rounding to three significant figures gives:

$\text{Area} \approx 33.2$ cm².

Here is triangle ABC - Edexcel - GCSE Maths - Question 16 - 2021 - Paper 2

Worked Solution & Example Answer:Here is triangle ABC - Edexcel - GCSE Maths - Question 16 - 2021 - Paper 2

Find the length of BC.

Find the area of triangle ABC.

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