Answer:
The distance across the river from Omkar and Big rock is 72 m
Step-by-step explanation:
We can solve this question using the sine rule
Melissa, Big Rock and Omkar are the vertices of a triangle, whose sides are 100 m , the distance across the river from Omkar and Big rock, and the distance across the river from Melissa and Big rock
∵ The sum of the measures of the interior angles of Δ is 180°
∵ The angle opposite to the distance across the river from
Omkar and Big rock is 33°
∵ The angle opposite to the distance across the river from
Melissa and Big rock is 98°
∴ 33° + 98° + m∠ opposite to the side of 100 m = 180°
∴ 131° + m∠ opposite to the side of 100 m = 180°
- Subtract 131 from both sides
∴ m∠ opposite to the side of 100 m = 49°
Now let us use the sine rule to find the distance across the river from Omkar and Big rock
Assume that x represents the distance across the river from Omkar and Big rock
∵ [tex]\frac{x}{sin(33)}=\frac{100}{sin(49)}[/tex]
- By using cross multiplication
∴ x × sin(49°) = 100 × sin(33°)
∴ x sin(49°) = 100 sin(33°)
- Divide both sides by sin(49°)
∴ x = 72.16537981
∵ x represents the distance across the river from Omkar and Big rock
∴ The distance across the river from Omkar and Big rock =
72.16537981 m
- Round it to the nearest meter
∴ The distance across the river from Omkar and Big rock is 72 m
