Please help me with this trigonometry real-world problem

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

∵

- 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

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)

graph them on a graphing calculator, press 2nd trace. select intersect. hit enter until it says answer. ti 84 works best

step-by-step explanation: