Question

"How are we ever going to build this bridge?" asks Omkar looking out across the raging river.

Answer 1

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.