If the magnitude of vector w is 48 and the direction is 235 degrees, we can find the vector w in component form by using trigonometry.
Let's denote the horizontal component as wx and the vertical component as wy.
The horizontal component, wx, can be found using the cosine of the angle:
wx = Magnitude × cos(Direction)
Substituting the given values:
wx = 48 × cos(235 degrees)
The vertical component, wy, can be found using the sine of the angle:
wy = Magnitude × sin(Direction)
Substituting the given values:
wy = 48 × sin(235 degrees)
Now we can calculate the values using a calculator or software. Rounding to two decimal places, we have:
wx ≈ 48 × cos(235 degrees) ≈ -32.73
wy ≈ 48 × sin(235 degrees) ≈ -32.00
Therefore, the vector w in component form is approximately (wx, wy) ≈ (-32.73, -32.00).
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