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ABC is a right-angled triangle - Edexcel - GCSE Maths - Question 7 - 2018 - Paper 3

Question 7

ABC is a right-angled triangle. AC = 14 cm. Angle C = 90° size of angle B : size of angle A = 3:2 Work out the length of AB. Give your answer correct to 3 signifi... show full transcript

Worked Solution & Example Answer:ABC is a right-angled triangle - Edexcel - GCSE Maths - Question 7 - 2018 - Paper 3

Step 1

Find angle A and angle B

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Answer

Let the measure of angle A be represented as 2x and angle B as 3x, where 2x + 3x = 90° (since it is a right triangle and angle C = 90°).

Thus, we have:

$5x = 90°$ $x = 18°$

Therefore, angle A = 2x = 36° and angle B = 3x = 54°.

Step 2

Apply trigonometric ratios

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Answer

Using the sine function, we can find the length of AB with:

$\sin(54°) = \frac{AC}{AB}$

Substituting to find AB:

$AB = \frac{AC}{\sin(54°)}$ $AB = \frac{14}{0.809}$ (approximately) $AB \approx 17.3 \, cm$

Step 3

Final answer

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Answer

The length of AB is approximately 17.3 cm, rounded to three significant figures.

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