ABC and ADC are triangles - Edexcel - GCSE Maths - Question 17 - 2017 - Paper 3

Using the formula for the area of a triangle:

$\text{Area} = \frac{1}{2} \times b \times h$

we can express the height from point D to AC as:

$56 = \frac{1}{2} \times AC \times 11 \times \sin(105°)$

Solving for AC gives:

$AC = \frac{56 \times 2}{11 \times \sin(105°)}$

Calculating this yields:

$AC ≈ 10.9$

Next, we apply the sine rule:

$\frac{AB}{\sin(27°)} = \frac{AC}{\sin(118°)}$

From this, we can solve for AB:

$AB = AC \times \frac{\sin(27°)}{\sin(118°)}$

Substituting in the value for AC:

$AB ≈ 10.9 \times \frac{\sin(27°)}{\sin(118°)}$

Calculating this results in:

$AB ≈ 4.3$

Thus, the length of AB, correct to 1 decimal place, is:

AB ≈ 4.3 m