A supporting guy wire is attached to the top of a utility pole and is fastened at the ground 10 feet from the base of the pole. If the angle between the guy wire and the ground is 8 times the angle between the guy wire and the pole, what is the measure of the angle between the guy wire and the ground?

I'm thinking I use pathag. theorem or sin cos tan? help?

Question

A supporting guy wire is attached to the top of a utility pole and is fastened at the ground 10 feet from the base of the pole. If the angle between the guy wire and the ground is 8 times the angle between the guy wire and the pole, what is the measure of the angle between the guy wire and the ground? 

I'm thinking I use pathag. theorem or sin cos tan? help?

whpalmer4 · Answer

I think you want to use sin/cos/tan here, because Pythagoras doesn't involve angles.  Or maybe there's something else we can do.

the base of the triangle is 10 feet.  The pole is presumably perpendicular to the ground (we can't solve the problem without assuming that), so the angle between the guy wire and the pole could be x and the angle between the guy wire and the ground is 8x.

anonymous · Answer

Yeah, that's what I have so far. But, I forgot the sin/cos/tan. thats the trouble im having

whpalmer4 · Answer

attachment

whpalmer4 · Answer

What do we know about the angles in a right triangle?

anonymous · Answer

add up to 180? and one is 90?

whpalmer4 · Answer

I think we have an easier approach here — the sin/cos/tan stuff won't work because we don't know enough measurements.

whpalmer4 · Answer

Right!  So if the angle between the pole and the ground is 90 degrees, what does that imply about x and 8x?

anonymous · Answer

8x+x+90=180?

whpalmer4 · Answer

yes.  Can you solve that for x?

anonymous · Answer

9x+90=180
9x+90-90=180-90
9x=90
9x/9=90/9
x=10

8(10)=80

whpalmer4 · Answer

so the angle between guy wire and the ground is?

whpalmer4 · Answer

(you've done the work correctly, but haven't labeled the results)

anonymous · Answer

80 degrees :) thank you! much simpler than i thought it was lol

whpalmer4 · Answer

and does that answer seem plausible, looking at the diagram, and considering all the utility poles you've encountered?

anonymous · Answer

Yes :) 10 degrees+80 degrees+90 degrees=180 degrees.

whpalmer4 · Answer

I think the lines aren't quite that steep in my experience, but definitely that seems like a more reasonable answer than 10 degrees, if we'd gotten ourselves mixed up on which angle was which.

anonymous · Answer

Yes lol :)

whpalmer4 · Answer

well, on to our respective next problems :-)