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Work out the length of AD - Edexcel - GCSE Maths - Question 18 - 2018 - Paper 3

Question 18

Work out the length of AD. Give your answer correct to 3 significant figures: AD can be calculated using the Law of Sines or the Law of Cosines based on the given t... show full transcript

Worked Solution & Example Answer:Work out the length of AD - Edexcel - GCSE Maths - Question 18 - 2018 - Paper 3

Step 1

Start of process to find the length of AD

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Answer

To find the length of AD, we first need to calculate angle B by using the fact that the sum of angles in a triangle is 180°.

Angle B = 180° - Angle A - Angle C = 180° - 86° - 34° = 60°.

Step 2

Process to find the length of AD

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Answer

Next, we can apply the Law of Sines:

$\frac{AD}{\sin(A)} = \frac{AC}{\sin(C)}$

From this, we have:

$AD = AC \cdot \frac{\sin(A)}{\sin(C)}$

Substituting the known values:

$AD = 12.5 \cdot \frac{\sin(86°)}{\sin(34°)}$

Calculating:

$AD = 12.5 \cdot \frac{0.998}{0.559} \approx 12.5 \cdot 1.784 \approx 22.3 cm$

Step 3

Final answer

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Answer

The length of AD, rounded to 3 significant figures, is 22.3 cm.

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