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 3 - 2017 - Paper 3

Now we can plug in the values:

$\sin x = \frac{13 \times \sin(50°)}{16}$

Using a calculator, we find:

$\sin(50°) \approx 0.7660$

Thus:

$\sin x \approx \frac{13 \times 0.7660}{16} \approx 0.6220$

Next, we find x by taking the inverse sine:

$x = \sin^{-1}(0.622) \approx 38.6°$

Additionally, since ( \sin \theta ) can give two angles in a triangle, we calculate:

$x = 180° - 38.6° \approx 141.4°$

Therefore, the two possible values for x are:

• 38.6°
• 141.4°

Both values should be rounded to one decimal place.