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Work out $$\sqrt{\frac{2.5 \times \sin{43^\circ}}{8.2^2 \times 0.5}}$$ Give your answer correct to 3 significant figures. - Edexcel - GCSE Maths - Question 8 - 2019 - Paper 3

Question 8

$Work-out--$$\sqrt{\frac{2.5-\times-\sin{43^\circ}}{8.2^2-\times-0.5}}$$--Give-your-answer-correct-to-3-significant-figures.-Edexcel-GCSE Maths-Question 8-2019-Paper 3.png$

Work out $$\sqrt{\frac{2.5 \times \sin{43^\circ}}{8.2^2 \times 0.5}}$$ Give your answer correct to 3 significant figures.

Worked Solution & Example Answer:Work out $$\sqrt{\frac{2.5 \times \sin{43^\circ}}{8.2^2 \times 0.5}}$$ Give your answer correct to 3 significant figures. - Edexcel - GCSE Maths - Question 8 - 2019 - Paper 3

Step 1

Calculate the numerator: $2.5 \times \sin{43^\circ}$

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Answer

Using the sine function, we find:

$2.5 \times \sin{43^\circ} \approx 2.5 \times 0.681998 = 1.704995$

Step 2

Calculate the denominator: $8.2^2 \times 0.5$

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Answer

First, find $8.2^2$ :

$8.2^2 = 67.24$

Then, multiply by $0.5$ :

$67.24 \times 0.5 = 33.62$

Step 3

Combine the results into the square root: $\sqrt{\frac{1.704995}{33.62}}$

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Answer

Now we compute the fraction:

$\frac{1.704995}{33.62} \approx 0.0507$

Taking the square root:

$\sqrt{0.0507} \approx 0.2253$

Step 4

Round to 3 significant figures

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Answer

Thus, rounding $0.2253$ to 3 significant figures gives:

$0.225$

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