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

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)

actually your concept is wrong

step-by-step explanation:

150% of x =300

150x=300×100

x=(300×100)÷150

x=200