ABC is a right-angled triangle - Edexcel - GCSE Maths - Question 7 - 2017 - Paper 3

Given triangle ABC with angle C = 23° and opposite side AC = 15 cm, we can use the sine function:

$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

Thus, we have:

$\sin(23°) = \frac{15}{AB}$

Rearranging the equation gives:

$AB = \frac{15}{\sin(23°)}$

Calculating:

1. First calculate ( \sin(23°) \approx 0.3907 )
2. Then, ( AB \approx \frac{15}{0.3907} \approx 38.39 , \text{cm} )

Finally, rounding to three significant figures:

$AB \approx 38.4 \, \text{cm}$