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The Sine Rule states:

April 28, 2026Mathematics

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Here are the solutions for each problem using the Sine Rule and other appropriate rules, with answers rounded to the nearest whole number.

The Sine Rule states:

\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

The sum of angles in a triangle is $180^\circ$ :

A + B + C = 180^\circ

The Cosine Rule states:

c^2 = a^2 + b^2 - 2ab \cos C

1) Given: $a = 24.5 \text{ cm}$ , $B = 44^\circ$ , $C = 76^\circ$

Find angle $A$ .
Using the sum of angles in a triangle:
$A = 180^\circ - B - C$ $A = 180^\circ - 44^\circ - 76^\circ$ $A = 180^\circ - 120^\circ$ $A = 60^\circ$
Find side $b$ using the Sine Rule.
$\frac{b}{\sin B} = \frac{a}{\sin A}$ $b = \frac{a \sin B}{\sin A}$ $b = \frac{24.5 \text{ cm} \times \sin 44^\circ}{\sin 60^\circ}$ $b = \frac{24.5 \times 0.694658}{0.866025}$ $b \approx 19.65 \text{ cm}$