The diagram shows triangle ABC - Edexcel - GCSE Maths - Question 13 - 2019 - Paper 2
Question 13
The diagram shows triangle ABC.
ADC and DEB are straight lines.
AD = 4.4 cm
BC = 8.6 cm
E is the midpoint of DB.
Angle CDB = 90°
Angle DCB = 40°
Work out the siz... show full transcript
Worked Solution & Example Answer:The diagram shows triangle ABC - Edexcel - GCSE Maths - Question 13 - 2019 - Paper 2
Step 1
Find DE
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Answer
Since E is the midpoint of DB, we can find the length of DE as follows:
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Answer
In triangle EAD, we have AD = 4.4 cm and DE = 4.3 cm. We can now use the tangent function to find angle EAD. Using the known angle DCB (40°), we find angle AED:
Angle AED = 90° - 40° = 50°
Now we can apply the tangent function:
an(EAD) = rac{AD}{DE}
an(EAD) = rac{4.4}{4.3}
Step 3
Calculate Angle EAD
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Answer
Now, we take the arctangent to find angle EAD:
EAD = an^{-1}igg( rac{4.4}{4.3}igg)
EAD ≈ 47.7°
Step 4
Final Answer
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Answer
Thus, the size of angle EAD is approximately 47.7°, when rounded to one decimal place.
