The diagram shows triangle ABC - Edexcel - GCSE Maths - Question 19 - 2019 - Paper 3
Question 19
The diagram shows triangle ABC.
AB = 3.4 cm
AC = 6.2 cm
BC = 6.1 cm
D is the point on BC such that size of angle DAC = \frac{2}{5} \text{ size of angle BCA}
Calcu... show full transcript
Worked Solution & Example Answer:The diagram shows triangle ABC - Edexcel - GCSE Maths - Question 19 - 2019 - Paper 3
Step 1
Calculate angle BCA
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Answer
To find angle BCA, we can use the sine rule in triangle ABC:
sin(∠ACB)AB=sin(∠ABC)AC
Let ( \angle BCA ) = ( x ), so ( \angle DAC = \frac{2}{5} x ).
Using the sine rule for the triangle ABC:
sin(x)3.4=sin(∠ABC)6.2
We need to solve for angle x using the known side lengths. We find angle ABC first.
Step 2
Find the size of angle DAC
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Answer
From the relationship we established:
∠DAC=52∠BCA
Therefore, once we find ( x ), we can compute ( \angle DAC ). Let’s find the values.
Step 3
Use the sine rule in triangle ADC
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Answer
For triangle ADC, we can again apply the sine rule:
sin(∠DAC)AC=sin(∠ACD)DC
Where ( DC ) is what we are trying to find, and ( \angle ACD = 180 - (\angle DAC + \angle ABC) $$. We can substitute the known values to find ( DC ).
Step 4
Calculate length DC
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Answer
After substituting the values through sine rule, we arrive at:
DC=sin(∠DAC)6.2⋅sin(∠ACD)
Substituting the values gives us the result. Make sure to round to three significant figures.
