A very formulaic trig word problem (find an angle)

[solve]

Homework Statement

A vacation resort in a mountain town has installed a zip line( a sturdy wire, down which costumers in harnesses can quickly descend from high altitudes) to attract patrons. One zip line is 1,750 feet long and allows its rider to descend from a ski slope down to the ground, a vertical drop of 450 feet. Calculate the angle of declension of the wire in radians, accurate to three decimal places.

Homework Equations

The Attempt at a Solution

I have a question about the drawing of this situation. I don't think I can draw it here so hopefully you can see what I am trying to draw from a little algebra work. See, the picture is drawn such that the angle works out to x=arcsin(9/35) from sinx=450/1,750. The top of the mountain is a plane.

I drew it in way that the angle works out to x=arccos(9/35) with adjacent side equaling 450 feet. In other words, my triangle is flipped upside down.

Why am I wrong? Thanks

 

[Infinitum]

The question asks you to find the angle of declination from the horizontal level.

The hill is something like this

|- -------------
|. -
|... -
|... -
|_____-

And you need to find the angle between the upper horizontal line and the slanted line. Your answer gives the angle between the slanted line and the vertical one.

 

[solve]

The question asks you to find the angle of declination from the horizontal level.

The hill is something like this

|- -------------
|. -
|... -
|... -
|_____-

And you need to find the angle between the upper horizontal line and the slanted line. Your answer gives the angle between the slanted line and the vertical one.

Oh, I see now. Thanks, Infinitum.

edit:

The question asks you to find the angle of declination from the horizontal level.

Let's say there was no picture that I could look up in relation to this situation. Would it be really wrong, then, to assume that there is no horizontal line on top of the mountain, because I really don't get the reference to that from the question? What if that was said explicitly? Would then the angle between the slanted line and the vertical one be considered the angle of declination? Thanks.

 

[Infinitum]

Let's say there was no picture that I could look up in relation to this situation. Would it be really wrong, then, to assume that there is no horizontal line on top of the mountain, because I really don't get the reference to that from the question? What if that was said explicitly? Would then the angle between the slanted line and the vertical one be considered the angle of declination? Thanks.

The angle of declination(depression) by definition means from a given horizontal level. This diagram should clear it up for you.

 

[solve]

Ah-huh! So the elevation angle would be the one between the horizontal line (the ground) and the sight line? Acute one? Obtuse one?

 

[Infinitum]

Yep. It might change to a different horizontal line depending on the problem, but it usually is the ground.

 

[solve]

Cool. In the drawing above which angle is the elevation angle? The obtuse one or the acute one?

Thank You.

 

[Infinitum]

As far as I know, elevation and depression angles are acute. It just doesn't feel right to let them be obtuse

 

[solve]

That's it, Infinitum. I appreciate your hep and thank you.

 

[Infinitum]

You're welcome!