Question

find bc
a) 23 km b) 21 km
c) 20 km d) 16 km

Explanation:

Step1: Find angle at B

In triangle \(ABC\), the sum of angles is \(180^\circ\). So, \(\angle B = 180^\circ - 38^\circ - 34^\circ = 108^\circ\).

Step2: Apply the Law of Sines

The Law of Sines states \(\frac{BC}{\sin A}=\frac{AB}{\sin C}\). We know \(AB = 22\) km, \(\angle A = 34^\circ\), \(\angle C = 38^\circ\). Plugging in: \(\frac{BC}{\sin 34^\circ}=\frac{22}{\sin 38^\circ}\).

Step3: Solve for BC

\(BC=\frac{22\times\sin 34^\circ}{\sin 38^\circ}\). Calculate \(\sin 34^\circ\approx0.5592\), \(\sin 38^\circ\approx0.6157\). Then \(BC\approx\frac{22\times0.5592}{0.6157}\approx\frac{12.3024}{0.6157}\approx20\) km (approximate, considering answer choices).

Answer:

C) 20 km