Answer:
The distance across the river from Omkar to the big rock is 72 meters.
Step-by-step explanation:
Using the given information draw as triangle as shown below.
According to angle sum property, the sum of interior angles of a triangle is 180°.
In triangle ABC,
\angle A+\angle B+\angle C=180^{\circ}
98^{\circ}+33^{\circ}+\angle C=180^{\circ}
131^{\circ}+\angle C=180^{\circ}
\angle C=180^{\circ}-131^{\circ}=49^{\circ}
The measure of angle C is 49°.
Sine formula:
\frac{a}{\sin a}=\frac{b}{\sin b}=\frac{c}{\sin c}
Using sine formula in triangle ABC, we get
\frac{AC}{\sin B}=\frac{AB}{\sin C}
\frac{AC}{\sin 33^{\circ}}=\frac{100}{\sin 49^{\circ}}
AC=\frac{100}{\sin 49^{\circ}}\times \sin 33^{\circ}
AC=\frac{100}{0.7547}\cdot0.544639
AC=72.166
AC\approx 72
Therefore the distance across the river from Omkar to the big rock is 72 meters.
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