GCSE Edexcel Maths Area & Perimeter: Here is triangle ABC. (a) Find

Here is triangle ABC - Edexcel - GCSE Maths - Question 15 - 2021 - Paper 2

Question 15

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 15 - 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, which states:

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

Here, let:

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

Substituting these values into the formula gives:

$BC^2 = 8^2 + 11^2 - 2 \cdot 8 \cdot 11 \cdot \cos(72°)$
$BC^2 = 64 + 121 - 176 \cdot 0.3090$
$BC^2 \approx 185 - 54.464 = 130.536$

Taking the square root:

$BC \approx \sqrt{130.536} \approx 11.4 \text{ cm}$

Therefore, the length of BC is approximately 11.4 cm.

Step 2

Find the area of triangle ABC.

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Answer

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

$Area = \frac{1}{2} \times base \times height$

In this case, we can also use the formula involving two sides and the sine of the included angle:

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

Substituting the known values:

$a = 8$ cm
$b = 11$ cm
$C = 72°$

So,

$Area = \frac{1}{2} \times 8 \times 11 \times \sin(72°)$
$\approx \frac{1}{2} \times 8 \times 11 \times 0.9511$
$\approx \frac{1}{2} \times 88.7856 \approx 44.3928$

Therefore, the area of triangle ABC is approximately 44.4 cm².

Here is triangle ABC - Edexcel - GCSE Maths - Question 15 - 2021 - Paper 2

Worked Solution & Example Answer:Here is triangle ABC - Edexcel - GCSE Maths - Question 15 - 2021 - Paper 2

Find the length of BC.

Find the area of triangle ABC.

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