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ABCD is a trapezium - Edexcel - GCSE Maths - Question 7 - 2017 - Paper 2

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Question 7

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ABCD is a trapezium. Work out the size of angle CDA. Give your answer correct to 1 decimal place.

Worked Solution & Example Answer:ABCD is a trapezium - Edexcel - GCSE Maths - Question 7 - 2017 - Paper 2

Step 1

1. Find the length of the third side of triangle ABC using Pythagoras' theorem

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Answer

In triangle ABC, AB = 7.5 cm and BC = 10 cm. To find AC, use the Pythagorean theorem:

AC=BC2−AB2=102−7.52=100−56.25=43.75≈6.6cmAC = \sqrt{BC^2 - AB^2} = \sqrt{10^2 - 7.5^2} = \sqrt{100 - 56.25} = \sqrt{43.75} \approx 6.6 cm

Step 2

2. Use trigonometry to find angle CDA

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Answer

In triangle CDA, we have:

  • opposite side = AC = 6.6 cm
  • adjacent side = AD = 24 cm

Using the tangent function:

tan⁡(CDA)=oppositeadjacent=6.624\tan(CDA) = \frac{opposite}{adjacent} = \frac{6.6}{24}

To find angle CDA:

CDA=tan⁡−1(6.624)≈15.3°CDA = \tan^{-1}(\frac{6.6}{24}) \approx 15.3°.

Rounding to 1 decimal place, the answer is approximately 15.3°.

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