A force of 200 N at 30° angle to the horizontal is used to drag an object 25 meters along the floor. Assuming that friction is zero, the amount of work done is best represented by ______.
a. cos 30° (25 meters) x 200 N
b. tan 30° (200 N) x 85 meters
c. sin 30° (25 meters) x 200 N
d. cos 30° (200 N) x 25 meters

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2015-08-16T00:10:01+08:00

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To produce work, force must be parallel to distance therefore, the answer is d.

Let me do a proof to let you remember quickly:
sin\theta =  \frac{x}{hypotenuse}
We know from trigonometric identity of tangent function is

tan\theta = \frac{sin\theta}{cos\theta}

To let you remember quickly, let me prove it to you that:

tan\theta= \frac{sin\theta}{cos\theta}= \frac{y}{x}

(Please be guided by the picture I uploaded)

tan\theta=\frac{sin\theta}{cos\theta}[\tex] ; [tex] cos\theta= \frac{adjacent}{hypotenuse} ; sin\theta= \frac{opposite}{hypotenuse} opposite = yadjacent=x
\therefore  tan\theta=\frac{ \frac{y}{hypotenuse} }{ \frac{x}{hypotenuse} }
tan\theta= \frac{y(hypotenuse)}{x(hypotenuse)}
\therefore tan\theta= \frac{y}{x}
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