Vector v has the given direction angle and magnitude. Find the horizontal and vertical components.
θ = 27° 30' |v| = 15.4

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Convert the direction angle from degrees and minutes to decimal degrees. Since 1 minute is \( \frac{1}{60} \) of a degree, calculate \( 27^\circ 30' = 27 + \frac{30}{60} = 27.5^\circ \).

Recall that the horizontal component (\( v_x \)) of a vector is found by multiplying the magnitude by the cosine of the direction angle: \( v_x = |v| \cdot \cos(\theta) \).

Similarly, the vertical component (\( v_y \)) is found by multiplying the magnitude by the sine of the direction angle: \( v_y = |v| \cdot \sin(\theta) \).

Substitute the given magnitude \( |v| = 15.4 \) and the converted angle \( \theta = 27.5^\circ \) into the formulas: \( v_x = 15.4 \cdot \cos(27.5^\circ) \) and \( v_y = 15.4 \cdot \sin(27.5^\circ) \).

Use a calculator set to degree mode to evaluate the cosine and sine values, then multiply to find the horizontal and vertical components of the vector.

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