The diagram shows a triangle ABC, AB is the shortest side - AQA - A-Level Maths Pure - Question 4 - 2022 - Paper 2

Substituting the known values into the sin rule yields:

$\frac{c}{\sin(38°)} = \frac{6.1}{\sin(A)} = \frac{8.7}{\sin(180° - A - 38°)}$

Now, let’s find the length of side AB (c).

Calculating: $c = \frac{8.7 \cdot \sin(38°)}{\sin(A)}$

Using the Sine Rule again:

Calculating angle A gives: $A = \arcsin\left(\frac{6.1 \cdot \sin(38°)}{8.7}\right) \approx 61° \text{ (rounded to the nearest degree)}$

Now, since angle A + angle B + angle C = 180°, we can identify the largest angle.

Calculating angle C: $C = 180° - A - 38° \approx 180° - 61° - 38° \approx 81°$

Thus, the largest angle in triangle ABC is approximately:

$119°$