A force of 8 N is exerted on a box. The component of this force which acts along the ground has a magnitude of 6.93 N, as shown below. What is the measure of angle x?

40°

50°

60°

30°

Question

A force of 8 N is exerted on a box. The component of this force which acts along the ground has a magnitude of 6.93 N, as shown below.  What is the measure of angle x?


 40°

 50°

 60°

 30°

hang254 · Answer

attachment

anonymous · Answer

You can use a trig function here. You know the adjacent side and the hypotenuse.

hang254 · Answer

which trig function would i use?

anonymous · Answer

SOH CAH TOA
You know "A" and "H"

hang254 · Answer

cos, adjacent, hypotenuse

anonymous · Answer

Correct, so you could use the cosine.

anonymous · Answer

$$\cos(x) = 6.93 / 8$$
Now just solve for x.

hang254 · Answer

.86625

anonymous · Answer

That's the value of the cosine there, but you want x. Not cos(x).
To get rid of the cosine, you can take the arccosine (acos, or cos^-1). Remember what you do to one side of the equation you must also do to the other.

anonymous · Answer

Well, actually that's not the value of cosine anywhere :P So I'm not sure what you did there. You want a degree measure, so be sure your calculator is in degree mode.

hang254 · Answer

29.974

anonymous · Answer

You got it. Or x is about 30 degrees.

hang254 · Answer

Thanks man :)

anonymous · Answer

De nada.