Answer:
To find the distance \( AB \) across the river, we can use the Law of Sines in triangle \( ABC \). From the problem, \( BC = 160 \) meters, [tex]\( \angle B = 109.3^\circ \)[/tex], and [tex]\( \angle C = 15.8^\circ \)[/tex].
First, we need to determine [tex]\( \angle A \)[/tex] in the triangle:
[tex]\[ \angle A = 180^\circ - \angle B - \angle C \][/tex]
[tex]\[ \angle A = 180^\circ - 109.3^\circ - 15.8^\circ \][/tex]
Once we have \( \angle A \), we can use the Law of Sines:
[tex]\[ \frac{AB}{\sin C} = \frac{BC}{\sin A} \][/tex]
[tex]\[ AB = \frac{BC \cdot \sin C}{\sin A} \][/tex]
Let's calculate these values.
The distance [tex]\( AB \)[/tex] across the river is approximately 53 meters.
Step-by-step explanation:
