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ABC is a right-angled triangle - Edexcel - GCSE Maths - Question 9 - 2018 - Paper 3

Question 9

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 signi... show full transcript

Worked Solution & Example Answer:ABC is a right-angled triangle - Edexcel - GCSE Maths - Question 9 - 2018 - Paper 3

Step 1

Using the ratio of angles A and B

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Answer

Let the size of angle A be represented as

$2x$

and the size of angle B as

$3x$ .

Since the sum of angles in a triangle is 180°, we can write:

$2x + 3x + 90° = 180°$

This simplifies to:

$5x = 90°$

Solving for x gives:

$x = 18°$ .

Thus, angle A is:

$2x = 36°$

and angle B is:

$3x = 54°$ .

Step 2

Applying trigonometry to find AB

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Answer

Using the sine function, we can express AB in terms of AC as follows:

$\sin(54°) = \frac{AC}{AB}$

Substituting the known length of AC:

$\sin(54°) = \frac{14}{AB}$

Rearranging the equation to isolate AB gives:

$AB = \frac{14}{\sin(54°)}$ .

Calculating this value:

$AB ≈ \frac{14}{0.809} ≈ 17.3 \, \text{cm}$ .

Step 3

Final answer

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Answer

The length of AB is approximately 17.3 cm, correct to 3 significant figures.

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