Question

Please help me with this trigonometry real-world problem

Answer 1

The distance across the river from Omkar and Big rock is 72 m

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

∵
`(x)/(sin(33))=(100)/(sin(49))`

- 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