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

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Work out the length of AD. Give your answer correct to 3 significant figures: A /| 11.4cm / | / | / | / | D-----B-----C 12.5... 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 establish the angle at D, which can be calculated using the formula:

extAngleD=180°−(34°+109°)=37° ext{Angle } D = 180° - (34° + 109°) = 37°

Step 2

Complete process to find the length of AD.

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Answer

Next, we can apply the Sine Rule, which is expressed as:

ADsin⁡(B)=DBsin⁡(D)\frac{AD}{\sin(B)} = \frac{DB}{\sin(D)}

In our triangle, we know:

  • BD = 12.5 cm
  • The angle B = 86°
  • The angle D = 37°

Thus, applying the Sine Rule:

AD=12.5⋅sin⁡(86°)sin⁡(37°)AD = \frac{12.5 \cdot \sin(86°)}{\sin(37°)}

Step 3

Process to find the length of AD.

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Answer

Substituting the values:

AD=12.5⋅0.998630.60182≈20.68cmAD = \frac{12.5 \cdot 0.99863}{0.60182} \approx 20.68 cm

Step 4

Final answer.

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Answer

Rounding 20.68 cm to three significant figures, we get:

AD≈20.7cmAD \approx 20.7 cm

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