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

Question 7

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

Using Pythagoras' Theorem

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Answer

To find the third side of triangle ABD, we can apply Pythagoras' theorem. The height from B to AD is 6 cm, and the base from A to B is 10 cm. Hence, the length of AB can be calculated as:

$AB = \sqrt{(7.5)^2 + (10)^2}$

Calculating gives:

$AB = \sqrt{56.25 + 100} = \sqrt{156.25} = 12.5 \text{ cm}$

Step 2

Finding Base Length of Triangle CDA

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Answer

To find the base length of triangle CDA, we know the total length AD is 24 cm. Subtracting the length of AB:

$CD = 24 - 10 = 14 \text{ cm}$

Step 3

Using Trigonometry to Find Angle CDA

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Answer

Now we can apply trigonometry to find angle CDA using the tangent function:

$\tan(CDA) = \frac{opposite}{adjacent} = \frac{6}{14}$

Calculating gives:

$CDA = \tan^{-1}(\frac{6}{14})$

Using a calculator, we find:

$CDA \approx 22.6^\circ$
Rounded to 1 decimal place, the final answer is:

$CDA \approx 22.6^\circ$

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