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 - 2016 - Paper 2

Rearranging the Sine Rule gives:

[ \sin x = \frac{16 \cdot \sin 50^ ext{°}}{13} ]

Calculating ( \sin 50^ ext{°} \approx 0.7660 ), we find:

[ \sin x \approx \frac{16 \cdot 0.7660}{13} \approx 0.943 ]

To find x, we take the inverse sine:

[ x = \arcsin(0.943) \approx 70.3^ ext{°} ]

However, since the sine function is positive in both the first and second quadrants, the second possible angle is:

[ x = 180^ ext{°} - 70.3^ ext{°} \approx 109.7^ ext{°} ]

The two possible values for x are approximately:

• ( 70.3^ ext{°} )
• ( 109.7^ ext{°} )