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In the triangle ABC, AB = 16 cm, AC = 13 cm, angle ABC = 50° and angle BCA = x° Find the two possible values for x, giving your answers to one decimal place. - Edexcel - A-Level Maths Pure - Question 4 - 2016 - Paper 2

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In the triangle ABC, AB = 16 cm, AC = 13 cm, angle ABC = 50° and angle BCA = x° Find the two possible values for x, giving your answers to one decimal place.

Worked Solution & Example Answer:In the triangle ABC, AB = 16 cm, AC = 13 cm, angle ABC = 50° and angle BCA = x° Find the two possible values for x, giving your answers to one decimal place. - Edexcel - A-Level Maths Pure - Question 4 - 2016 - Paper 2

Step 1

Find the sine of angle BCA

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Answer

Using the sine rule, we have: sin⁡x16=sin⁡50°13\frac{\sin x}{16} = \frac{\sin 50°}{13} This implies: sin⁡x=16⋅sin⁡50°13\sin x = \frac{16 \cdot \sin 50°}{13}

Step 2

Calculate the value of sin(x)

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Answer

Calculating this gives: sin⁡x=16⋅0.766013≈0.943\sin x = \frac{16 \cdot 0.7660}{13} \approx 0.943

Step 3

Determine possible angles x

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Answer

Now, we find the possible values of x:

  1. First angle: x=arcsin⁡(0.943)≈70.5°x = \arcsin(0.943) \approx 70.5°
  2. Second angle: x=180°−70.5°≈109.5°x = 180° - 70.5° \approx 109.5°

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