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ABC is a right-angled triangle - Edexcel - GCSE Maths - Question 7 - 2021 - Paper 2
Question 7
ABC is a right-angled triangle. (a) Work out the length of BC. Give your answer correct to 1 decimal place. PQR is a right-angled triangle. (b) Work out the size ... show full transcript
Worked Solution & Example Answer:ABC is a right-angled triangle - Edexcel - GCSE Maths - Question 7 - 2021 - Paper 2
Step 1
Work out the length of BC.
Answer
To find the length of BC, we can use the tangent function which relates the opposite side to the adjacent side in a right triangle. In triangle ABC:
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Given that angle A = 56° and AC = 12 cm, we have:
\tan(56°) = \frac{BC}{12} -
Rearranging this gives:
\ BC = 12 \times \tan(56°)
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Calculating this:
\ BC = 12 \times 1.4826 \approx 17.8 cm
Thus, the length of BC is 17.8 cm.
Step 2
Work out the size of the angle marked x.
Answer
In triangle PQR, we are given PQ = 18 cm and QR = 15 cm. We can use the sine function to find the angle x:
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The sine function is defined as:
\sin(x) = \frac{opposite}{hypotenuse} = \frac{QR}{PQ}
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Thus:
\sin(x) = \frac{15}{18}
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Calculating the angle:
\ x = \sin^{-1}\left(\frac{15}{18}\right) \approx 56.3°
Therefore, the size of the angle marked x is 56.3°.