Answer:
The distance across the river from Omkar to the big rock is 131343149 meters
Explanation:
* Lets study the information in the problem
- Let Omkar position is point A
- Let Melissa position is point B
- Let big rock position is C on the other side of the river
* Now we have triangle ABC
- The distance between Omkar and Melissa is 100100100 meters
along the river
- The angle between Omkar and the big rock is angle BAC
∴ m∠BAC = 33°
- The angle between Melissa and the big rock is angle ABC
∴ m∠ABC = 98°
- The big rock is at angle C
* Now we can find the distance between Omkar and the big rock
by finding the length of side AC in the triangle
- By using the sine rule
∵ sin A/BC = sin B/AC = sin C/AB
∵ AB = 100100100 meters
∵ m∠ABC = 98°
- Lets find m∠C
∵ In any triangle the sum of the measures of the interior angles is 180°
∴ m∠A + m∠B + m∠C = 180°
∵ m∠A = 33° , m∠B = 98°
∴ 33° + 98° + m∠C = 180° ⇒ add
∴ 131° + m∠C = 180° ⇒ subtract 131 from both sides
∴ m∠C = 49°
- Now lets use the sine rule
∵ sin ABC/AC = sin C/AB
∴ sin 98/AC = sin 49/100100100 ⇒ by using cross multiplication
∴ AC = (sin 98 × 100100100) ÷ sin 49 = 131343148.8
∴ AC ≅ 131343149 meters
* The distance across the river from Omkar to the big rock is
131343149 meters