For sin 30° = 0.5
For one of the sine rule with values substituted,
$$ rac{6.5}{ ext{sin } 30°}$$
For \( \angle ABC \) = $$\frac{6.5}{65} \times 30°$$ - Edexcel - GCSE Maths - Question 22 - 2022 - Paper 1
Question 22
For sin 30° = 0.5
For one of the sine rule with values substituted,
$$ rac{6.5}{ ext{sin } 30°}$$
For \( \angle ABC \) = $$\frac{6.5}{65} \times 30°$$.
or for a ... show full transcript
Worked Solution & Example Answer:For sin 30° = 0.5
For one of the sine rule with values substituted,
$$ rac{6.5}{ ext{sin } 30°}$$
For \( \angle ABC \) = $$\frac{6.5}{65} \times 30°$$ - Edexcel - GCSE Maths - Question 22 - 2022 - Paper 1
Step 1
For sin 30° = 0.5
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Answer
First, we establish that for many trigonometric calculations, knowing the primary values is crucial. The value of sin 30° is widely recognized as 0.5.
Step 2
For one of the sine rule with values substituted,
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Answer
Next, we can substitute the known values into the sine rule. Using the formula:
sinAa=sinBb
where ( A ) is the angle opposite side ( a ) and ( B ) is the angle opposite side ( b ). For our problem, substituting gives us:
sin 30°6.5=sin ABC65
Step 3
or for a complete process to find \( \angle ABC \),
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Answer
To isolate ( \angle ABC ), we can manipulate the sine rule equation:
sin ABC=656.5×sin 30°
Thus,
sin ABC=656.5×0.5
Step 4
Answer of \( \frac{3.25}{10.7} \) = 6.5 part 3 marks.
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Answer
Therefore, when calculating with the given values, the mathematical evaluation leads to:
10.73.25≈0.3037
This result contributes toward the overall understanding of sine rules in trigonometry.
Step 5
Where \( [D] \) is their value of sin 30°.
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Answer
The sine value of 30° is critical as it serves as a benchmark in various trigonometric functions and calculations.
Step 6
Answer must be in the form \( \frac{m}{n} \) where m and n are integers.
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Finally, ensure that the final answer is presented as a fraction of integers, satisfying the condition of being in the format ( \frac{m}{n} ).
