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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

Sagot :

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

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

[tex]tan\theta = \frac{sin\theta}{cos\theta} [/tex]

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

[tex]tan\theta= \frac{sin\theta}{cos\theta}= \frac{y}{x} [/tex]

(Please be guided by the picture I uploaded)

[tex]tan\theta=\frac{sin\theta}{cos\theta}[\tex] ; [tex] cos\theta= \frac{adjacent}{hypotenuse}[/tex] ; [tex]sin\theta= \frac{opposite}{hypotenuse} [/tex] ; [tex]opposite = y[/tex] ; [tex]adjacent=x[/tex]
[tex]\therefore tan\theta=\frac{ \frac{y}{hypotenuse} }{ \frac{x}{hypotenuse} } [/tex]
[tex]tan\theta= \frac{y(hypotenuse)}{x(hypotenuse)}[/tex]
[tex]\therefore tan\theta= \frac{y}{x} [/tex]
View image DaneGil1996