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The diagram shows triangle ABC with D on AC and E on AB - OCR - GCSE Maths - Question 14 - 2017 - Paper 1

Question 14

The diagram shows triangle ABC with D on AC and E on AB. DE is a straight line. AD = 28 m, AE = 41 m, DE = 22 m and BC = 64 m. Calculate the length CD.

Worked Solution & Example Answer:The diagram shows triangle ABC with D on AC and E on AB - OCR - GCSE Maths - Question 14 - 2017 - Paper 1

Step 1

Calculate angle ADE

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Answer

To find angle ADE, we can use the cosine rule:

ext{cos} ext{A} = \frac{AD^2 + AE^2 - DE^2}{2 \cdot AD \cdot AE}

Substituting the values:

ext{cos} ext{A} = \frac{28^2 + 41^2 - 22^2}{2 \cdot 28 \cdot 41} = \frac{784 + 1681 - 484}{2296} = \frac{1981}{2296}

Calculating gives us:

$ext{A} \approx 38.30^{\circ}$

Step 2

Using sine rule to find CD

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Answer

Now, we apply the sine rule in triangle ADE:

Rearranging gives us:

Calculating the sine values and substituting:

$CD \approx 22 \cdot \frac{0.9511}{0.6161} \approx 33.1 m$

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