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Here is triangle ABC - Edexcel - GCSE Maths - Question 14 - 2020 - Paper 2

Question 14

Here is triangle ABC. Work out the length of AB. Give your answer correct to 1 decimal place.

Worked Solution & Example Answer:Here is triangle ABC - Edexcel - GCSE Maths - Question 14 - 2020 - Paper 2

Step 1

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Answer

To find angle ACB, we can use the angles in a triangle sum property. The sum of angles in a triangle is 180 degrees.

Thus,

$\text{Angle ACB} = 180^\circ - 26^\circ - 34^\circ = 120^\circ$

Step 2

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Answer

Using the Law of Sines, we can set up the following relationship:

$\frac{AB}{\sin(34^\circ)} = \frac{23.8}{\sin(120^\circ)}$

Step 3

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Answer

Rearranging the formula to solve for AB:

$AB = 23.8 \times \frac{\sin(34^\circ)}{\sin(120^\circ)}$

Calculating the values:

Calculate $\sin(34^\circ)$ and $\sin(120^\circ)$ :
- $\sin(34^\circ) \approx 0.5592$
- $\sin(120^\circ) \approx 0.8660$
Substitute these values in:

$AB \approx 23.8 \times \frac{0.5592}{0.8660} \approx 15.3 \text{ cm}$

Thus, the length of AB is approximately 15.3 cm, correct to 1 decimal place.

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