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In the diagram below, ABCD is a trapezium - OCR - GCSE Maths - Question 19 - 2017 - Paper 1

Question 19

In the diagram below, ABCD is a trapezium. Length AE is 37.5cm. DE = CF Find the value of angle x. A -------------- B E /| / | D--C | | | ... show full transcript

Worked Solution & Example Answer:In the diagram below, ABCD is a trapezium - OCR - GCSE Maths - Question 19 - 2017 - Paper 1

Step 1

Find length DE or CF

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Answer

Using the trapezium properties, we see that triangles ADE and BCF are similar. Thus, we have:

$DE = CF = 62.5cm - 37.5cm = 25cm$

Step 2

Set up sine relationship

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Answer

For triangle ADEF, we can use the sine ratio:

$\sin(x) = \frac{DE}{AD}$ Where AD is the hypotenuse. Given AD is calculated using Pythagorean theorem:

$AD = \sqrt{(62.5^2 + (37.5^2))}$

Step 3

Calculate angle x

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Answer

Using inverse sine, we calculate:

$x = \sin^{-1}\left(\frac{25}{AD}\right)$ Substituting the values for DE and AD gives the final angle measurement.

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